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In this sample, only the first Ancient Element (AIR) is available. The other Elements, WATER, EARTH and FIRE, are included in the complete hypertextbook, and each of those Elements are about twice as long as AIR. To learn more about the course and hypertextbook, visit the Principles of Alchemy (Chemistry) website.
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The "air" of the universe, hydrogen and helium.

Isotopes are the variations of the elements.

Transmutation changes the elements.

Dalton: creator of Modern Atomic Theory.

The symbols & hieroglyphics of Modern Chemistry.

Nuclear Radiation: The types of atomic energy and how we count it.

Creation of all the atoms in the Universe.

Bohr's shells are the first step to understanding electrons.

Atoms are shaped by their orbitals.

It's just quantum mechanics!

The universe is full of hydrogen. In most places it is rather sparsely distributed, as in the vacuum of space. But in some places hydrogen is so thick that it creates stars. Hydrogen is the first of the elements. It's the oldest, the smallest, the simplest and the most abundant of the elements. It makes up over 74% of the Universe! Another element, helium, makes up another 24%. So together, hydrogen and helium, the "air" of the universe, make up 98% of everything there is. Understand them and you will understand 98% of the chemistry of the universe! That is the goal in our first lesson.

Wow. What does hydrogen look like?

Hydrogen is an atom and atoms are very, very small. Invisible. Atoms are the smallest units of matter that keep their chemical identity. The name "atom" is from the Greek for "indivisible", because you cannot break up an atom any further and still have a chemical.

What would you have if you broke up an atom?

Sub-atomic particles, not a chemical. It wasn't until late in the 19th century that people started thinking that there might be something smaller than an atom. We still use the Greek word "atom" even though it is made of smaller particles.

It's convenient to imagine atoms as tiny spheres around which orbit smaller spheres (dots!) of opposite electrical charge. This is a sufficient and workable image on which to build an understanding of Modern Alchemy (chemistry). Be warned, however, that this picture of atoms breaks down at the level of detail and understanding required by physics.
But for the purposes of Alchemy it is good to think of hydrogen as a single, positively charged sphere called a proton. Protons are in all atoms. Hydrogen IS a proton. And that is why hydrogen, the first element, is also the simplest, smallest and most abundant element. Hydrogen is the fundamental element upon which the Universe is built!

Thatís it?! Hydrogen is just a positive bit of tiny, invisible matter?

Aye. But at the temperatures and conditions at which most chemistry takes place, these protons (hydrogen) have a companion particle called an electron. Electrons carry a single negative charge, equal but opposite to the proton's charge. And electrons are much smaller than protons. It would take over a thousand electrons to give you the same mass as one proton. The hydrogen's electron orbits the proton, being attracted to it by the opposite charge, but restricted from actually reaching it (by laws best dealt with in an advanced physics class). Notice that the positive charge of the proton is balanced by the negative charge of the electron, so the entire hydrogen atom has a "net" charge of zero.
Like this: +1 (proton) and -1 (electron) gives a total charge of 0. That's a complete, neutral hydrogen atom.

Do you mean to say that most of the Universe is made of just a single positively charged proton, with a single negatively charged electron?

Not quite. Most of the hydrogen in the universe is ionized. That is, the number of electrons is NOT equal to the number of protons. An atom which has an UNEQUAL number of protons and electrons is called an ion. Ions always have a "net" charge. Either positive, if it has more protons than electrons, or...

... or negative if it has more electrons than protons!

That's right. Stars are mostly hydrogen ions because they are so hot that the electron flies off! These hydrogen ions have a charge of +1.

Because only the proton with its positive charge is left.

Time for a review. Everything in the universe is made of atoms. The simplest, smallest and most common atoms are hydrogen. It has a single positive proton and often a single negative electron circling it. That gives the hydrogen atom a net charge of zero. If the hydrogen is very, very hot, like in a star, it looses its electron. It will have a net charge of positive one (+1) from that one proton and we say it is ionized.
Because hydrogen is so simple, I like to say that hydrogen is the first element.

Hey, whatís an "element"? You never really said!

Didnít I? Oh dear. Well, elements are substances made entirely of atoms with the same number of protons. Chemicals are made of elements and elements are made of atoms. Gold is an element. If you break up a piece of gold, it gets smaller and smaller until all that is left is a single gold atom. If you cannot break it down any further, you know you have an element.

So a gold coin is made of nothing but gold atoms? Gold is an element?

Aye, it is! A coin of pure gold is a pure element. You can break it into smaller gold pieces, but you cannot break it into anything else.
Hydrogen is the most common element and gold one of the rarest.

What if something is made of different kinds of atoms? You know, atoms with different numbers of protons.

That would be a compound. Compounds are made of two or more elements. Water is a compound because, if you work at it, you can break it up into two different types of atoms or elements. In your next lesson I will teach you about water. Today I want to keep things simple and just talk about elements and the atoms that define them.

OK. So, elements are an Alchemistís fundamental working material?

Yes, precisely! There are about a hundred different elements, gold and hydrogen just being two of them.

And if you tried to break up the atoms of an element, all you would get would be protons and electrons, which arenít atoms or elements themselves and arenít chemicals either!

Yes, thatís right. Oh, but you would also get some neutrons out of most atoms or elements which you broke up.


Yes. They are the other things inside atoms. Neutrons are at the center of the atom, along with the protons, and they are about the same size as a proton. But neutrons do not have a charge.

Neither positive nor negative?

Aye. Thatís why we call it a neutron. Itís neutral. I like to think of neutrons as the ghosts of atomic particles. They hide in the center of the atom along with the protons, but you canít detect them by their charge. They contribute nothing to the atomís chemistry. Theyíre just extra mass. That brings us to an important point.
Protons define the element.
Hydrogen is hydrogen because it has one proton. Gold is gold because it has 79 protons.

The number of protons tells you what element it is?

Yes! And it's the number of protons which give an atom its chemical properties.
Hydrogen behaves the way it does because it has only one proton. Gold behaves the way it does because it has 79 protons.
The chemical behavior of each and every element is determined by the number of protons, and the number of protons defines what the atom or element is called. The number of protons in an atom is the atom's atomic number.

So if an atom had a million and one protons, it would have an atomic number of a million and one?

Yes, that's right. But you'll never find an atom with that many protons. The biggest naturally occurring atom has an atomic number of 92.

So it has 92 protons! And those 92 protons cause it to behave in a certain way. Simple.

Yes, it is. Alchemy isn't difficult.

But some Alchemists are!

Enough of that!
You can see that the atomic number is the first thing you would want to know about an atom, because it tells you how many protons it has and thus what element it is and how it behaves.

What about those neutrons?

Oh. Neutrons do nothing to define the element and they have nothing to do with the atomís chemistry. They add extra "weight". But I like to think of them as adding extra mass. Weight is just an "earthly" term. We Alchemists speak of the mass not the weight of atoms. More on that later.

But hydrogen doesnít have any neutrons. Right?

Ah, well, sort of right.
Most hydrogen is just a proton, but some hydrogens have a neutron too. As a matter of fact, some even have two neutrons. But they are still hydrogen...

... because they all have only one proton!


We say they are isotopes of hydrogen. Isotopes of an element have the same number of protons (thatís why they are a single element) and have the same chemistry (because they have the same number of protons). But isotopes have different masses because they have different numbers of neutrons.

But they're all called hydrogen.

Ah, sort of. Because hydrogen is the most common element, people decided to give names to the hydrogen isotopes. It is fair to call all hydrogen isotopes hydrogen, but we can be more specific. If the hydrogen has one neutron, it is called deuterium and if it has two neutrons we call it tritium.

And if it doesnít have any neutrons, just a proton, it is called hydrogen?

Yes. It seems strange, but the element called hydrogen (which always has just one proton) can have no neutrons, one neutron, or two neutrons. The hydrogen with no neutrons, doesnít have a special name, but the two other hydrogen isotopes have names of their own. Strange isnít it?

And confusing.

It gets easier. But you must understand that all elements are defined by the number of protons. The various isotopes of each element differ only in the number of neutrons.

Isotopes of an element always have the same number of protons but can have a wide number of neutrons. Got it.
What would you call an atom with two protons?

That would be helium and Iím glad you brought that up. Helium is the second smallest, second oldest and second most abundant element (or atom) in the universe. Helium is identified by having two protons.

And I bet it comes with different numbers of neutrons.

You bet right. Fortunately, the different helium isotopes do not have their own names. Helium can have either one or two neutrons. But helium can never have no neutrons.

Why not?

Good question. Helium atoms without a neutron are too unstable to last. They disappear faster than you can blink!


Because there are certain combinations of protons and neutrons which work and some that donít. It all has to do with the way they interact in the center of the atom, the nucleus (plural nuclei). The exact reason is understood by only a handful of physicists and is not important to understanding Alchemy. But a good Alchemist is aware that some isotopes are stable and some are not. Some, like helium without a neutron, disappear instantly, while others like tritium take years to disintegrate.


I donít know. I suspect it has something to do with the "magical" world of sub-atomic physics. I am not trying to teach you that anyway. Letís stick to Alchemy, shall we?

OK. Are all the hydrogen isotopes stable?

No. Tritium disintegrates. But slowly. It takes about 12 years for half of it to disintegrate. And another 12 years for half of that to disintegrate. And so on.

What does it disintegrate into? What does tritium become?

First, let me tell you about this kind of disintegration and then you can tell me what tritium becomes when it disintegrates. This is called beta decay and here is how it works.
Tritium has a proton and two neutrons, right?


One of tritiumís neutrons turns into a proton. It's like magic!
Now tell me, if that tritium atom turns one of its neutrons into a proton, what element has it become?

Ah, letís see. If weíre talking about an element we are talking about the number of protons. Tritium has one proton (thatís why itís hydrogen). But if it were to get another proton, it would have two. So it would become helium.

Right. Tritium disintegrates (or decays, if you like) into helium.

One element is turned into another?

Aye. And it is amazing! In medieval times such as these, wizards and kings would give anything to change one element into another. Even the best Alchemists canít do that. But nature does it all the time. And always at a constant rate.

What is this magic called?

Transmutation (and it is NOT magic). When one element becomes another it is transmuted. This is an unusual angle on chemistry, and is really a topic for physics. But any good Alchemist should be aware that it occurs.
Now hereís a thought. The mass of the old tritium and the new helium are the same, because protons and neutrons have the same mass. Thereís a total of three particles in each.
Nothing has really changed except the charge.

OK, fine. You canít get something out of nothing. Youíve always taught me that.

And it always applies.

Oh, yeah. Then what about the extra positive charge? When one of tritiumís neutronís becomes a proton it doesnít get any extra weight. But it does get a positive charge for free! Right?

That would be right if that were the end of the story, but it's not. The total charge, or "net" charge, remains unchanged because as the tritium turns a neutron into a proton, it also makes an electron and spits it out!

I see. So the charges balance each other out. But where does the electron's weight, the "mass" as you call it, come from? You just said that neutrons and protons weigh the same. So where does the electronís mass come from? Huh? Huh? Huh?

OK! OK! I was trying to keep this simple you know. Iím trying to teach Alchemy here not physics!

But I want to know! You canít get away explaining that the newly formed protonís positive charge is balanced by a new electron. All you have done is explain it away by creating another mystery. You haven't explained the mass of the newly created electron. Youíve always taught me to never be satisfied with a half answer. I want to know where that electronís mass has come from when tritium beta decays into helium. Where does it get the mass to make the electron it splits out?!

Well, the truth is, the mass of the neutron is very slightly heavier than that of a proton.
And before you start to give me more trouble, let me repeat, Iíve been trying to keep this simple!
So when the neutron turns into a proton, the electron is created from the difference in mass. And the opposite charge of the new electron balances out the positive charge of the new proton. All is in balance. Nothing is created from nothing! All I want you to understand is that the (very slightly heavier) neutron disintegrates into a proton and electron. Which together means that no new charges or mass are created, just rearranged. Do you understand?

I think so. One of the neutrons in tritium turns into a proton and an electron. Because an extra proton is created, the nucleus now has two protons and so it is no longer the element hydrogen. It has been transmuted into the next element, helium. And an electron is spit out too, so there is a balance of charge. Because you canít get something from nothing! Even the mass is the same because the mass of the new proton plus the mass of the new electron equals the mass of the old neutron. Right?

By Jove, I think youíve got it! Now, I want you to think about that electron again. I said it was spit out of the nucleus. Remember?

Yeah. Where does it go?

It goes flying far away. It escapes from the newly formed helium like a rocket! That electron moves away at such a tremendous speed that it can cause damage if it hits you. You do not want to get hit by too many of these flying electrons!

So the helium is dangerous?

No. Youíve got it backwards. It's the tritium that is dangerous because it spits out a fast moving electron as it decays into helium. The tritium is unstable, but the helium it becomes is stable. When an isotope transmutes (changes from one element to another), it spits out particles and rays, and we say it is radioactive. It is that "radioactivity" which is dangerous. Got it?


Good. So tell me what you have learned about beta decay of tritium and its transmutation into helium.

Radioactive tritium, a radioactive isotope of the element hydrogen, decays into helium, by producing a proton from its extra neutron. And it also makes an electron which it spits out so fast that it can hurt you.

Thatís right. Now letís put some names and numbers to how we describe these things. The protons and neutrons, the two things in the atom's nucleus, are called nucleons. Nucleons make up most of the mass of an atom, the rest of the mass is just the very light electrons. When we talk about the mass of an atom, we are only referring to the total number of nucleons. We don't count the electron's mass. Normal hydrogen with its one proton has a mass of one. It has only one nucleon. Deuterium, has two nucleons (one proton and one neutron) for a total mass of two. How many nucleons does tritium have?

Three - one proton and two neutrons.

Right! So the element Hydrogen has three isotopes - with one, two or three nucleons. But they are all the same element because each of those three isotopes have only one proton.

If we were to weigh them we would find that the tritium weighs three times as much as the normal hydrogen. And a normal hydrogen would weigh only half that of a deuterium atom. Do you understand why?

Yeah. Because the normal hydrogen has only one nucleon, deuterium has two and tritium three. Simple addition.

We think of the hydrogen atom (actually its proton, because that's all there is to normal hydrogen) as the fundamental unit of chemistry.
And this is a good point to mention units. You know, how we count in chemistry.
Rather than talk of something's weight, we think in terms of its mass. Mass is a much better way of describing something. The weight of something can easily change without the atoms changing. All you have to do is take it away from the Earth or move it around rapidly. But its mass doesn't change. Its chemistry is still the same. The mass is constant! The mass of a hydrogen (proton) is exactly One Dalton.

Says who!

Says Dalton! He was a genius. Lived just a few miles from here. John Dalton was one of England's great natural philosophers. In 1808 he wrote a book called New System of Chemical Philosophy. It changed the way we think about matter and was a critical step in the evolution of Ancient Alchemy into Modern Alchemy (chemistry).

What! A philosophy book!?

Well, it was! But it was not like most philosophy books. Dalton argued that for each chemical element there is a different kind of atom. He explained that different materials are different combinations of these atoms. Dalton was so important that Alchemist use his name for the fundamental mass of atoms.

So hydrogen has a mass of one Dalton because it has only one proton.

Correct. Protons and neutrons each have a mass of a Dalton. Or close enough. (Don't start on me about the tiny difference in weight between the proton and neutron!) Put another way, the mass of a nucleon, either proton or neutron, is one Dalton. What is the mass of the other isotopes of hydrogen?

Easy. Deuterium has a proton and a neutron, so a deuterium atom weighs two Daltons.

Not "WEIGHS"! It has "a MASS OF" two Daltons. It might weigh ten pounds in one part of the universe and nearly nothing somewhere else. But deuterium always has a MASS of two Daltons.

OK. OK. I get it. So tritium, has a MASS of three Daltons.

Now you've got it!
What have you learned so far?

Protons define the element. And nucleons (protons and neutrons) define the "mass" , which is measured in Daltons.

The atom's atomic mass is the number of nucleons it has.
Don't get it confused with an atom's atomic number, which is the number of protons it has.
Tell me, what are the atomic number and atomic mass of helium?

Well helium has two protons so it has an atomic number of two.

Correct. And helium's atomic mass?

Ah, four! Because it has two protons and two neutrons so its total nucleon count is four.

Is it? Is it always? Do all helium's have an atomic mass of four? Do all helium atoms have four nucleons?

Well. I don't know. Maybe not. It might have only one neutron for a total of three nucleons.

That's right! You see, helium ALWAYS has an atomic NUMBER of 2....

...because it always has two protons.

Right. But helium doesn't always have two neutrons.

Oh, I see. It might have only one neutron. Or maybe dozens! But it would still be helium, because it has only two protons. So helium's atomic MASS could be anything!

Sorry if you feel I have mislead you. I want you to see what you can and cannot figure out directly from knowing what element it is. Atomic NUMBER tells you the ELEMENT, but atomic MASS tells you the ISOTOPE.

I see. The atomic number of an element is always the same for that element and is the number of protons. The number of protons define what element it is, and how it behaves.

That's right. But the atomic mass of an element...

Could be anything!

Almost anything. The atomic mass can never be smaller than the atomic number. Do you know why?

Oh, I see. The atomic mass is the total of all the nucleons, including the protons. So if an atom has ten protons, it must have an atomic mass of at least ten. Maybe more, but never less.


Simple. Atomic mass tells you the isotope and atomic number tells you the element.
So you tried to trick me by asking me the atomic mass of helium. You can't tell from just knowing it is helium. Except it would have to be two Daltons or more. But you can't tell exactly unless you know the number of neutrons in it.

That's right. But it wasn't a trick. It was an example of what you can figure out if you know what you are doing.

OK. But does this mean that I will never know the atomic mass of an atom? I can't just look at it and see the neutrons. At least I can tell how many protons it has by the way it behaves - by its chemistry. But I can't know the number of neutrons because neutrons don't affect the chemistry.

That's right. Sort of.
In the 20th century they have ways to measure the atomic mass of atoms. But we will often refer to an atom's mass, its atomic mass, as if we had measured it. The mass of all the elements, actually their various isotopes, can be found in any good chemistry book.

But, is there an "average" isotope? Is there a way to approximate its mass? It would make things easier

Yes, it would and yes, there is. It's called relative atomic mass and here's how it's calculated. We measure all the helium isotopes and figure out how much of each is present in the universe and in what proportions.

In the whole universe?

No, not really. We estimate the relative proportion of the element's isotopes and come up with a number which represents its relative atomic mass.

How's that done?

With sophisticated machines in the 20th century. It works like this. An extremely pure sample of the element is weighed and its mass calculated. Because the sample contains a representation of all its isotopes, each of a different mass and occurring in different proportions, it acts as an "average" for all the isotopes.

I'm confused.

An example might make it clear.
As it turns out, the most common isotope of helium has four nucleons, or an atomic mass of four.

OK. But what about the helium atoms with only one neutron, with an atomic mass of three?

Well, all the other helium isotopes are much, much rarer. But they do make a contribution to the total population of helium. So it would be wrong to ignore them. Let's say, just for this example, that for every 1000 helium atoms with an atomic mass of four Daltons, there is one helium atom with an atomic mass of three Daltons. If you were to measure the mass of all 1001 of those helium atoms, and then divide by 1001, you would get the average atomic mass for that collection of helium atoms. Right?

Sure. It's simply an average. Weigh 1001 atoms and divide that weight by 1001 will give you the average weight. I mean mass!

Yes, indeed!
Tell me. What would be the total mass of 1000 helium atoms with four nucleons plus that one lighter helium with only three nucleons?

Four Daltons times a thousand is four thousand (4 X 1000 = 4000) and that one lighter helium atom gives an extra three Daltons. So all 1001 of those helium atoms weigh, I mean have a mass of, 4003 Daltons.

Yes. Now what would be the average mass for those atoms?

Well, I just divide 4003 by 1001 (4003 / 1001 = ) to get ....... hmmm.. that's a difficult division. I need some paper.

You can do it if you like. But tell me, will it be four?

Ah.... No. The total mass of all 1001 atoms would have to be 4004 to give you a whole number like 4.
Actually, the answer will be a little less that 4. You know, 3.99999 something.

That's right! 3.999000999 to be exact. (Don't ask me how I do those big numbers. It helps to have a 20th century calculator!)

So the relative atomic mass for helium is 3.999000999.

Yes, it would be. But only if there were 1000 heliums with four nucleons for every one helium with only three nucleons. However, the universe is more complex. I've used the 1000 to 1 ratio to make the math easy.

You call that easy?!

It could be worse. The ratio of those two isotopes of helium is a lot larger than 1000 to 1. And we haven't considered the other helium isotopes. You know, the ones with five or six nucleons (three or four neutrons).

Sounds complex.

It is. But not difficult to understand. 20th century Alchemists have sampled parts of the earth and some parts of space and they have worked out the ratios of all these elements. They have calculated the relative masses of each element from that data.

So, what's the atomic mass, I mean RELATIVE atomic mass of helium?


But that's larger than four.

Yes, it is. What does that tell you about the isotopes of helium?

It means there must be more of the heavier helium isotopes than the lighter ones.

Absolutely right.
Each element has a "most common isotope". Helium's most common isotope has four nucleons and it has an atomic mass of 4 Daltons. But when you average in all the other isotopes of helium, each in the proportions found in the universe, you get the relative atomic mass of 4.0026.

Nice. Very accurate. Is it useful?

Sometimes. But not usually.

What? Why have you bothered to teach me about it?

Because in some forms of Alchemy it IS important. And when you look up the relative atomic mass of an element (in one of my 20th century books) you will understand how it can have numbers which are not whole numbers.
Believe me Arthur. By learning these basics with simple atoms, like hydrogen and helium, you will have the ability to do it for the more complex atoms. You'll see.

OK. I'll remember how relative atomic mass is figured out and how to use it later.


We've been using a rather awkward way to describe these atoms. I think it's time I taught you how to talk and write like a proper Alchemist!

Like saying "abracadabra"?

Not quite.
Like saying "helium four" instead of saying "helium with four nucleons". It is easier to say. Don't you think so?

Yeah. So is tritium, just hydrogen three?

By Jove, yes it is! What's another name for deuterium?


Right. Easy isn't it?

Yeah. Just name the element and its nucleon number.

Now let's talk about how we go about writing down these isotopes and elements.
First, we abbreviate the elements. Hydrogen is simply "H".
Second, we list the number of nucleons in the element just above and to the left of the letter. Like this: 1H. That's simply hydrogen with one nucleon. And that nucleon has to be a proton, or it wouldnít be hydrogen. Right?


Now deuterium has a proton and a neutron. So it has two nucleons and we abbreviate deuterium as 2H. By the way, we pronounce this "hydrogen-two", even though it is written with the number first. If we called it "two hydrogen", people might think we were talking about two hydrogen atoms, not a type of hydrogen.

I see. So deuterium is 2H or "hydrogen-two".

Tell me, Arthur. How would you abbreviate tritium?

Letís see. Tritium has three nucleons so it is 3H. And I'd call it "hydrogen three".

Right. This simple way of abbreviating the atoms allows us to describe them better. The letter reminds us which element we are talking about and the number of nucleons tells us which isotope.
Recall, it is the number of protons which determines the way the element behaves. But it is the total nucleon count which tells us itís mass. Hydrogenís three isotopes are 1H, 2H and 3H.

So these three isotopes make up most of the universe?

About 74% of the mass of the universe is hydrogen. And 99.985% of that hydrogen is the simplest type, the 1H. Only 0.015% of the hydrogen is 2H (deuterium).

Hey! Wait a minute. If 99.985% of the hydrogen is 1H (regular hydrogen) and 0.015% is 2H (deuterium), that adds up to 100%. What about the 3H (tritium)?

Good question. Tritium is very, very rare! So rare that it doesnít show up in the count. It would take a lot of zeros to show it as a proper number. Weíll talk about that some other time. For now, letís just say there is only a tiny trace of tritium around.

OK. What about helium?

You read my mind. That was to be my next topic.
Helium makes up about 24% of the universe. So together hydrogen and helium account for 98% of the mass of the entire universe. Those two elements make up so much of the universe, I like to think of them as the air of the universe.

Tell me more about helium. What is helium's abbreviation? It canít be "H" because we use that for hydrogen.

Thatís right. There are about a hundred different elements, so we have to use two letters for some to avoid duplication. The abbreviation for helium is "He". And it has four possible isotopes. Can you tell me how they would be abbreviated?

Well, they would all use the abbreviation "He". But I donít know what the nucleon count would be.

Think about it. Think about the structure of heliumís nucleus and the nucleons it is made of.

Well, helium must have two protons. Thatís why it is helium. So I guess the first helium isotope would be 2He.

Thatís a good guess, but not correct.


Sorry Arthur. Your thinking is correct, but an atom containing two protons with no neutrons is so unstable that it disappears in the blink of an eye. Remember, I talked about that earlier

Oh yeah. 2He is unstable. Like tritium.

Not quite. Tritium takes years to decay. Tritium is unstable, but at least it lasts long enough to find it (if we want to). But 2He is so unstable it disappears before anyone can see it. In fact, Iím not even sure it exists at all!

Oh, I see.
Well, if helium needs a neutron to stabilize its nucleus, then the minimum number of nucleons would be one neutron and two protons for a total of three. So 3He is the first helium isotope. Right?

Absolutely right. And it just so happens that 3He is what tritium (3H) becomes. Remember?

Oh, yeah. Tritium is radioactive and it decays into helium with two protons and a neutron. I remember.

I bet you can even draw a picture showing how tritium decays into helium. Go ahead and try. Just use an arrow to show which way it goes as it disintegrates.

OK. Tritium (3H) changes one of its neutrons into a proton to make the helium (3He). So that would look like this
3H ------> 3He

Yes. Very good. Now add the electron that is created. Abbreviate the electron as e (for electron) and just to remind you that the electron has a negative charge, put a tiny minus sign on it.

OK, so it would be
3H ------> 3He + e-

Excellent. Now to really complete it, why not put all the charges in the right place.
Remember, a hydrogen nucleus has a single proton so it would have one positive charge and helium has two protons so it would have two positive charges. Just place them to the upper right of each element.

Like this?
3H+ ------> 3He+2 + e-

Perfect! What you have written is called an equation. An Alchemist's equation is a way to write down a change or a reaction. In this case we have an equation for a transmutation.
Specifically, this equation is the equation for beta decay.
By the way, the equation you have written is for very hot elements - too hot to have their normal electrons circling them. At normal temperatures hydrogen would have one electron circling it and helium would have two electrons. Can you write that equation to include the electrons that normally circle them.

Sure. I'll just add them in like this
3H+ + e- ------> 3He+2 + e- + e- (created by the beta decay)

Very good. Now why not tidy things up by adding up those electrons on the right? It will look nicer.

Like this?
3H+ + e- ------> 3He+2 + 2e-

That's exactly right. And very professional too. What you have written is a complete equation. Notice that you can add those electrons together, just like anything else. 2e- is the same as e- + e-. One electron was there to begin with (it was with the hydrogen you started with) and the other one was made by the beta decay.
(Of course, in beta decay the newly created electron is thrown out, away from the atom, but here I am just talking about the numbers of electrons involved.)

And it all makes sense! On the left the tritium's positive charge, due to its one proton, is canceled out by its one electron. And on the right, helium's two protons, with their total charge of +2, is canceled out by the two electrons. The equation shows that extra charges have been created but they cancel each other out!
(In "real" beta decay the newly created electron is thrown out, away from the atom, so this helium would actually have a positive charge but here I am just talking about the numbers of electrons involved in order to keep track of the numbers.)

Yes indeed!

I see. So nothing comes from nothing. The equation shows we are just rearranging the charge and nucleons!

Yes! And that is a fundamental part of understanding chemistry. We Alchemists write balanced equations all the time. Sometimes like these, but often with other elements and their electrons. All we do when we write a balanced equation is show how it started and how it ends up.

I got it!

Good. We will be using equations a lot as you learn Alchemy. The equation you have just written is for beta decay and it is a particularly difficult one because it is an equation for a NUCLEAR reaction.
By the way, many people mispronounce the word "nuclear". They say it like "newk-lee-ear" or "new-klee-ear".

Yeah, that's they way a lot of people say it.

A lot of people are wrong. "Nuclear" has only two syllables. It's pronounced "new-klear".
A proper Alchemist speaks properly!

OK, "new-klear". That's difficult to get your tongue around!

Well, it just takes a little practice. Especially if you've been mispronouncing it for years! I think it has to do with the way we say "nucleus" (pronounced "new-klee-us") and "nucleon" (pronounced "new-klee-on").

OK, "new-klear" , "new-klear" , "new-klear" , "new-klear" , "new-klear" , "new-klear"...

You've got it!! (Phew!)
In the future we will be writing equations for CHEMICAL reactions. Only in nuclear reactions do you have transmutations of elements and "creation" of new atomic particles. Equations for chemical reactions are easier because the elements don't change and it is easier to understand.

So, you made me do a difficult equation I am unlikely to use in the future! Thanks a lot!

You're welcome!
The reason I directed you to write the equation for beta decay, a nuclear reaction, is because it is a good learning experience. If you can write an equation like that, with all its complex transmutations and "creation" of new particles, then you will have no trouble writing chemical equations.
But today I want to finish our discussion on isotopes.
Now then, 3He is heliumís first isotope, but I said helium had four isotopes. Can you describe the rest.

Well, I suppose they must all differ by the number of neutrons, because they canít have anything other than two protons or they wouldnít be helium. (Theyíd be something else.) If heliumís first isotope has one neutron, then Iíll guess that the next isotope would have two neutrons. That would give it a total of four nucleons (two protons and two neutrons) and I would describe that isotope as 4He.

Absolutely right. And the other two helium isotopes?

Ah, letís see. If it had three neutrons it would have a total of five nucleons so it would be 5He. And if it had four neutrons it would have six nucleons so it would be 6He.

Right again. You have just described all four of heliumís isotopes. And, just in case you are wondering, there are no helium isotopes with more than four neutrons. They just arenít stable long enough to be found. 7He does not exist nor does any other helium of higher nucleon count. I donít know why not. Just a limit on how many neutrons you can cram into a helium nucleus, I guess.

But do other elements have more than 6 nucleons?

Oh yes indeed! But for this lesson I want us to focus just on the two elements of hydrogen and helium and their isotopes. Any questions?

Yeah. Which of heliumís four isotopes is the most common?

That would be 4He. It makes up nearly 100% of all helium. There is a very tiny amount of 3He and that comes from the disintegration of tritium (3H) during beta decay. The other isotopes of helium are so very rare that you would have to search a huge amount of space to find them. And youíd have to look very fast too because both 5He and 6He are radioactive. They decay in less than a second.

So Iím wasting my time learning about them!?

No. Not at all. You have proven to me that you understand how to describe isotopes. And you will use that knowledge throughout the entire world of Alchemy. If you learn how to describe the isotopes of hydrogen and helium, you should be able to describe the isotopes of all the other elements.
Now, where was I? Hmmmm.
Let me review for you the abundance of the universeís most common elements and isotopes.
Hydrogen makes up 74% of the universe and 99.985% of that is simply 1H (just a proton) with deuterium (2H) making up most of the rest and (radioactive) tritium as just a tiny trace.

And over the years 3H beta decays into 3He, heliumís lightest isotope.

Right. But 4He is the isotope of helium you are most likely to find.

So, about 74% of the universe is made of 1H and 24% of 4He. The other 2% of the universe is made of other elements and some of the rare isotopes of hydrogen and helium.

Yes exactly. Now you know 98% of the stuff the universe is made of. Any more questions?

Yeah, about radiation. Who discovered it? And how? Radiation is invisible, right?

Yes, radiation is invisible and that certainly made it hard to discover. But not impossible. In 1896 a French scientist named Henri Becquerel (pronounced "beck-er-L") was working with a mineral called pitchblende. He didn't know it at the time, but pitchblende is radioactive. One day Becquerel accidentally placed a key between one of his pitchblende samples and a piece of photographic film.

What's "photographic film"?

Ah, yes. Photographs and film. Hmmm...
In the 19th century folks discovered that light, just a ray of light, could cause chemical reactions in a silver solution. It's a very interesting reaction, really, but I don't want to get into it now. Suffice it to say that photographic films are coated with chemicals which can detect light. Like a chemical version of an eye. OK?


Anyway, Becquerel later used that plate, and when he developed it he discovered an image of the key on it!


Real weird. Becquerel had no explanation for that image. Finally he decided that some invisible particles or light rays from the pitchblende penetrated the photographic container and caused the plate to be exposed. But the key had blocked some of the "light" so a shadow of the key was made.

So Becquerel discovered radiation by accident?

Aye. But Becquerel was smart enough to figure out what was going on. His discovery lead the way to many important inventions. And his discovery increased our knowledge of many things - from the universe to atoms.

Is beta decay the only kind of radiation? And is tritium the only radioactive substance?

No, there are two other forms of radiation and many different types of radioactive substances beside tritium.

What other forms of radiation are there?

Beta radiation is just one kind of radiation. The other two are called alpha and gamma radiation. We wonít encounter them until we start to study other, heavier elements. Besides, they are more in the area of physics than chemistry.

But what are these alphas and gammas? They sound like ancient Greek letters.

Thatís where the names come from. Of course the Greeks had no idea about radiation. Radiation wasnít discovered until the 20th century. And as it was discovered, the three types were named after those three Greek letters. They were named based upon their ability to pass through matter.

Like a ghost?

Sort of. (But remember, thereís no such thing as a ghost!)
Alpha particles are very weak and cannot pass through a piece of paper. Even your skin can block them.
Beta particles are a bit stronger. They can pass through skin and some can even go through a book!

What are these particles anyway?

Actually we have discussed them already.
Alpha particles are actually fast moving 4He, with no electrons. So alpha particles have a positive charge from the two protons.

A +2 charge?

Yes. Exactly. And beta particles are fast moving electrons. So they have a negative charge of -1.

That's what is spit out of tritium when it decays.

Right. And that is why we call it beta decay. In beta decay a high speed electron is spit out of the nucleus. In alpha decay a high speed helium nucleus is spit out. Many different elements have isotopes which produce alpha and beta radiation - spitting out alpha particles (4He-2) or beta particles (e-).

And what about the gamma radiation?

Gamma rays are extremely powerful and it takes very thick bricks to stop them. Gamma isnít a particle at all. It is a high energy ray of light.

Let me see if I got this straight. There are only three kinds of radiation and they are named by how well they pass through a substance.

Yes. Now it is your turn to tell me the three types of radiation.

Alpha particles are the weakest and are just a helium atom stripped of its electrons, so it has a positive charge (+2) because of the two protons.
Beta particles are more powerful and are just electrons, so they have a single negative charge (-1).
And gamma rays are not particles at all, just very powerful rays of light which can pass through lots of things.

Very good!

How often do these radioactive substances decay?

They do it all the time. Nothing can stop radioactive decay. Not even freezing it. The rate of decay is not affected by the chemical or physical state of the sample.

No, no. I mean, how long does it take to get rid of all the radioactivity?

Oh. Well that depends on the particular radioisotope. And that brings us to the subject of half-life.

Half life! I thought life was all or nothing. You can't have a half life.

No, YOU can't have a half life. And neither can I, but a radioisotope can have a half-life (notice the hyphen). The rate at which a radioactive sample decays, its half-life, depends on the specific radioisotope.
Take tritium (3H) as an example. It has a half-life of about 12 years.

And that means...?

And that means, half of a sample of tritium will have decayed after 12 years. So if you start with 1,000 atoms of tritium, in twelve years you would have only 500 atoms of tritium left. And you would have 500 atoms of something else. Can you tell me what those 500 atoms of something else would be?

I suppose they are the left over helium atoms (3He) produced by the decay of tritium.

You "suppose" very well. After 12 years, half of the tritium would have been transmuted to helium-3.

And what about the other 500 tritiums?

Well, they are tritium and they will do what tritium always does, beta-decay into helium-3. So in 12 more years half of those 500 tritium atoms will have decayed into more helium-3.

Leaving only 250 tritiums.

Yes, exactly. After a total of 24 years those 1,000 tritium atoms would have decayed into 750 helium-3 atoms, with only 250 of the original tritium atoms left. That's because 24 years is TWO half-lives for tritium. After each half-life, only half the original radioisotope remains. And that's why we call it "half-life". It's the time it takes half of the radioisotope to decay.
Now tell me how much tritium there would be in each successive 12 year interval. Start with 1,024 tritium atoms.

OK. In 12 years you would have half of 1,024 or 512 tritium decays, producing 512 helium-3 atoms and leaving 512 tritiums to continue decaying.
In another 12 years half of those 512 tritiums would have decayed away, leaving only 256 tritiums.
Another 12 years (36 years from when we started) would leave only 128 atoms of tritium.
Then another half-life goes by so 12 years later you have only 64 tritiums. Then 32, then 16, then 8, then 4, then 2 and then just 1 tritium left. I suppose that decays in 12 years too.

Another good supposition. But the funny thing about radioactive decay is that it is all a matter of probability. With 1,024 tritium atoms, you can be confident that about 512 will have decayed after 12 years. Just like you would be confident that if you flipped a coin 1,024 times it would come up heads about 512 times. But if you only had one coin flip, it might come up heads or tails. One or the other, but you don't know which. That's the problem with probabilities. They can trick you up sometimes. Especially when you are thinking about just one event. Like one coin flip or one tritium decay.

Sounds complicated.

Well, frankly, some folks understand the problems with probability immediately and others don't. But the important thing to understand is that you don't really work with one or even 1,000 atoms at any one time. You work with billions! So it doesn't really matter about the small numbers problem and the probabilities.

So, you're wasting my time.

No! I'm teaching you both the theory and the practice of Alchemy. A good Alchemist knows both.

There are other radioisotopes beside tritium, right?

Yes and they each have their own half-life. That is, each radioisotope decays at its own rate.

Which cannot be changed. Not even by freezing it. Right?

That's right. You have been paying attention, haven't you? Let's consider another radioisotope.
Carbon-14 (14C) has a half-life of almost 6000 years (5770 years to be exact). Tell me, if I waited 12,000 years, how much of the original carbon-14 would remain?

That's easy. Half!
No wait. Half of half. Because it has gone through two half-lives (12,000 years = 2 X 6,000 years). So it would have only a quarter of its original radioactive substance left.

Yes. I'm glad you caught your error there. In fact we can write down a series of ever smaller fractions to represent the half-life decays. All radioisotopes decay by half during each half-life. So after each half life we have half of what we started with.
Use 1 to represent the "fraction" of radioisotope we start with (actually the 1 means ALL the atoms are the radioisotope). Then we get a series of fractions like this: 1, 1/2, 1/4, 1/8, 1/16, 1/32,........

And it goes on forever!

Yes, or very close to forever. By doubling the number under the fraction line (the denominator) we are halving the entire number. See?

I think I get it. Give me another radioisotope.

OK. Potassium-40 has a half-life of 1.3 billion years.

What! That's ridiculous!

No. That's a fact. Some radioisotopes are very patient. Others are not and they have half-lives measured in fractions of a second. It all depends on which radioisotope you are dealing with. So, if I had a rock with only 1/8 as much potassium-40 as it had when it was made (from molten lava), how old is that rock?


Oh, you can do this Arthur. All I'm doing is turning the problem around. If the rock has only 1/8 as much potassium-40 as it started with, how many half-lives have gone by.

Oh, I see. Well, just a half-life back in time it would have had 1/4 of its radioactivity. And a half-life before that it had half (1/2) its radioactivity. And a half-life before that it had all its radioactive potassium-40.
Let's see, that means it went through, one half life (to get to 1/2), then a second half-life (to get to 1/4) and a third half-life to get to 1/8. So that rock sat through three half-lives.

Yes. So, how old is it then?

Ah, three half-lives at 1.3 billion years each half-life is 3.9 billion years. (3 X 1.3 billion years = 3.9 billion years)

That's right! The rock is 3.9 billions years old. Get it?

Yeah. I get it. Just figure out how many half-lives have gone by and multiply that by the length of one half-life to figure out how long it has been decaying. But how radioactive is a rock?

That depends on the rock. Some are very radioactive and some are not very radioactive at all. We measure radioactivity using a 20th century device called a Geiger counter (pronounced "Guy-ger" counter).

Named after some guy named Geiger I assume.

Aye! A Geiger counter counts the number of particles given off by a radioactive substance. The exact way it does that is best left for a physics class. However, we all express the amount of radioactivity in a substance by the number of disintegrations it has each second.

Do we call each unit of disintegration a "Geiger"?

No (but that's a good guess).
Becquerel's discovery with pitchblende got the attention of a French husband and wife team, called the Curies. They built on his work and found two new radioactive elements, polonium (Po) and radium (Ra). We named the unit of radiation after them. I'll spare you the details. But they studied huge amounts of radioactive decay. One gram of the radioisotope they studied, radium-226 (226Ra), produces 37 billion disintegrations per second. We now call that much radioactivity a Curie (abbreviated "Ci").
One Curie (Ci) equals 37 billion disintegrations per second (abbreviated "37 bdps").

Wow! That's a lot of radioactivity.

Yes it is!. We express it as Curies per gram (of rock, or gas, etc.) And that brings us to our last radioactive word. Specific activity is the number of Curies per gram.

So, a one gram rock which gives off 37 billion disintegrations each second has a specific activity of one. As a matter of fact, one gram of pure radium-226 (whatever that is) has a specific activity of one. By definition!

Yes. Very good. And if you had a one gram rock which gave 18 and a half (18.5) billion disintegrations per second...

... it would have a specific activity of one half.

Correct. Now suppose you had a 100 gram rock which gave off 370 billion disintegrations per second (370 bdps). What would be its specific activity?

Ah, that's a harder one. But I can do it!
That 100 gram rock has 100 grams (obviously) producing 370 billion disintegrations per second.

But we express specific activity in "Curies per gram", not "Curies per 100 grams".

I know. I know!
So only one gram of that rock would be producing 3.7 billion disintegrations per second. (I just divided 370 bdps by 100 grams to get the number of disintegrations produced by just one gram of the rock).
So one gram of that rock produces only 1/10 of a Curie (3.7 bdps divided by a full Curie, which is 37 bdps, equals 1/10 of a Curie).
So that rock has a specific activity of 1/10 (or 0.1).

Yes, but 1/10 of what? What are the units of specific activity?

Oh, Curies per gram! So I suppose I should say that the rock has a specific activity of 0.1 Curies per gram.

Yes. You're absolutely right! You sound like a real scientist when you say it that way.
It's always a good idea to think of the units you are dealing with whenever you are working on a scientific math problem. It makes what you are talking about clearer.

It's easy to get lost in this kind of thinking. I lose track of where I am in the math, sometimes.

We all do! The trick is to work your math slowly and orderly. Each person goes about their math work in a different way. But as long as it is clear to them (and correct) then that is fine.

How do YOU do YOUR math work? With that "calculator" from the 20th century?

Well, yes and no. Calculators help. Especially with complex numbers. But calculators are worthless if you don't know what you are doing. That's why it is good to write things down in an orderly manner. And be particularly careful with your units. Be sure you haven't forgotten an important step.

OK. But how DO you do your math work?

I lay out the problem as a series of steps, and see if it makes sense. Then I do the calculations. I'll use the previous problem as an example. (This is MY way of doing the same problem. That's not to say that you did it wrong because you did it differently.)
First I ask myself, "What do I have?" ("What do I know?") and "What do I want?" ("What do I want to know?").

You "have" a 100 gram rock producing 370 billion disintegrations per second. And you "want" the specific activity.

That's right. The next step is to recognize the connection between what I "want" and what I "have". In this problem it is the units of specific activity that makes the connection.

How's that?

Well the units of specific activity are "Curies per gram". Right?


And a Curie is 37 billion disintegrations per second. Another way of saying that is, 1 Curie EQUALS 37 billion disintegrations per second.

Yeah, I'm with you so far. (I think.)

Good. Now I line the units up in order to go from what I have to what I want.
The rock is 100 grams and produces 370 billion disintegrations per second.
I'm going to write that as "370 bdps/100 grams".

That's 3.7 bdps per gram!

Yes it is. But let's not move too quickly. Let's also remember the units we want to have at the end of it all. We want the answer to be in Curies per gram, because that's what specific activity is! So we must "convert" disintegrations per second into Curies.
Conversions are a very important part of science math problems. Some people panic when they see "conversion problems". They really don't need to panic. Besides, the panic just makes things worse! If they think about the units involved in any conversion, it all goes very smoothly and clearly.

How do you mean?

Well, one Curie equals 37 bdps. I'm going to write that as "37 bdps = 1 Curie". If you have been following my thinking you can now line up my "thoughts" into a single math statement. Try it.

OK (but I'm not sure what you are trying to do).
37 billion disintegrations per second = 1 Curie (37 bdps = 1 Curie)
Specific activity is expressed as Curies per gram (Curie/gram)
and the rock is 100 grams producing 370 bdps.

Very good. Now line them up in such as way as to get rid of the numbers and units I don't need while keeping the ones I want.

How can you get rid of the units you don't need?

By converting them. I do that by remembering that any number divided by itself is 1. Also I remember that any number multiplied by one is unchanged. Those two rules are the most important rules in mathematics!

Yeah, even I know that anything divided by itself is one! And multiplying by one is a useless exercise!

Not useless. Useful! You'll see why in a moment. Now, have you thought that 37 billion disintegrations divided by a second equals one?

One what?!

37 billion disintegrations divided by one second equals one. One Curie! Remember?

Ah, yeah. So what?

So, one equals 1 Curie divided by 37 billion disintegrations per second.
That's written as "1 = 1 Curie/37 bdps".

I see. All you've done is move it around to make the one equal to something related to the problem. To the conversion that is.

Yes. Exactly. Now, let's get back to the problem.
That 100 gram rock produces 370 billion disintegrations per second.
And, "1 = 1 Curie/37 billion disintegrations per second".
Now, what would happen if I multiplied the 370 billion disintegrations per second in that 100 gram rock, by 1?

Just multiplying by one does nothing. It is unchanged.

Yes you are right. It "does nothing" and it is unchanged. But we can do something and change the number if, instead of multiplying by one, we multiple by "1 Curie/37 bdps". When we do that we are just multiplying by one because "1 = 1 Curie/37 billion disintegrations per second". That's the same as 1, but it allows us to convert our problem into the units we want.

But multiplying by "1 = 1 Curie/37 billion disintegrations per second" is just dividing by 37 billion.

That's right. Now let's write this all out as an "equation".
370 bdps/100 grams (that's the rock)
multiplied by
1 Curie/37 bdps.

That's 370 bdps/100grams times 1Curie/37bdps or another way of saying it is
(370bdps/100grams) X (1Curie/37bdps)

Yes. And now you have your answer!

No, I don't! Where?

Let's write it as a proper math expression. It will make it more obvious.

The Rock

370 bdps
100 grams



The Conversion

1 Curie
37 bdps



The Answer (almost)

10 Curies
100 grams



The Answer (finally)

0.1 Specific activity

Notice that the bdps above and below the fraction line "cancel each other out".

Yeah, because you can slide the numbers left and right along the fraction.
So really you could have written that equation as 370 bdps/37bdps = 10.

Yes you could have. And the bdps disappears because you are dividing something by itself (bdps/bdps =1). That leaves you with just a clean "10".

And the part "Curies/100grams" that's still there? What about it?

Oh, yes. We divide that 10 from above, by the 100 grams of rock to give 0.1 Curies/gram. And that is our answer. The specific activity is 0.1 Curies/gram.

It looks like a long way to go for a simple answer.

Well, it is a disciplined way to do the problem. And it works for me! It lets me keep track of the units and lays it all out in a clear manner.

Must I do the math your way?

No. If you have a way that works for you and you are happy with it, then stick with it. However, I've found that by lining up all the information, and juggling the math around to reflect what I am trying to get at, I arrive at the right answer every time.
And speaking of time, I think it is time to end this lesson. Any final questions about atoms?

Yeah. Where did atoms come from? How were they made?

Oh, goodness! You do like to tackle the big questions don't you?
The universe and everything in it started many billions of years ago in a Big Bang!

An explosion?

Yes. But not your typical explosion. It was an explosion from nothing that created everything.

What?! Sounds like magic - or nonsense.

Yes, it does. It isn't quite magic, but it is about as close as science gets to magic! And I assure you it isn't nonsense either. I don't want to get into the details of exactly how this Big Bang came about. It's a very specialized subject and I'm not sure I fully understand it myself! Suffice it to say that out of this huge explosion came all the protons, neutrons and electrons which make atoms.

All kinds of atoms were created by the Big Bang?

No, just the smallest and simplest elements were made directly from the Big Bang. The vast majority of atoms created were just hydrogen and helium, with all their various isotopes. That's why they are so common.

The "air of the universe".

Yes. But there was also a trace of the next heavier elements: lithium, beryllium and boron.

Oh, new elements! What's their atomic number? And their abbreviations? Are they difficult to learn?

It's very simple really. These next three elements were the ones to have more protons (and neutrons and electrons).
Lithium has 3 protons and is abbreviated (Li).
Beryllium has an atomic number of 4 and is abbreviated (Be)
And boron has 5 protons and is written as simply (B)

How many neutrons does each have?

Well lithium usually has 4 neutrons.

So it has an atomic mass of 7. Usually.

Yes. Most lithium, but not all lithium, has 4 neutrons, which along with the 3 protons (which define it as lithium) give it an atomic mass of 7 Daltons. However, some lithium has only 3 neutrons.
But, see here, I don't want you to try to memorize ALL the various isotopes. It's good to know the isotopes of hydrogen and a few special isotopes. But it will be a waste of your time to memorize them all. You can always look up their atomic mass later. If you need to. No Alchemist goes far without his "Handbook of Chemistry". Recall, it is the number of PROTONS that really matter.

Yeah, yeah, I know. So, from this Big Bang came the first 5 elements?

Yes, that's right. Also, some were made in a process called "nuclear synthesis" which means the creation of nuclei.

How? With what?

With the starting material of the Big Bang - the hydrogen and helium mostly. And the "how" was (and still is) "nuclear fusion"

OK. Now you're just giving me names without meaning. What's nuclear fusion?

As the name implies, nuclear fusion is a reaction in which the nucleus of one atom fuses with the nucleus of another.

I see. And by adding together two atoms, you add together all the protons that were in them. So you build heavier elements using the light ones.

Yes. Exactly. In the process you also make an awful lot of energy. Lots of gamma rays!

Sounds dangerous. And this still goes on? Inside stars?

Yes indeed. The main nuclear fusion reaction is the fusing together of two hydrogen atoms to get helium. The leftover energy powers the sun! And most of the other stars in the universe too.

But there was already helium from the original Big Bang.

Yes, and the universe is making more helium as it powers the sun and stars. But I see you are getting anxious to learn how the heavier elements were formed.

Probably from more nuclear fusions, using heavier elements than hydrogen.

That's right. As a star grows old it uses up its hydrogen. Eventually there is nothing but helium in the star. Then the star shrinks and starts to slam the heliums together...

... creating atoms with 4 protons. Beryllium!
But, hey, there was beryllium created in the Big Bang too.

Yes, but I haven't finished my story. Two berylliums can get slammed together to make an element with 8 protons, oxygen. Oxygen makes up about 20% of our atmosphere.

You mean the air we breath was made inside a star?

Yeap. And so were most of the atoms in your body. The carbon atoms, with 6 protons are the result of fusing other smaller atoms.

Like by fusing two lithium atoms (atomic number 3) or a helium and a beryllium (atomic numbers 2 and 4). Either way you get 6 protons.

Right. The exact nuclear reactions are not important for us to go into. But, as you can see, it is simply a matter of slamming atoms together, fusing their nuclei, and getting new elements. There are also a lot of unstable nuclei formed and they rapidly decay into more stable forms, giving off all three forms of radiation as they rearrange their new nuclei.

Nuclear fusion is another form of transmutation!

Yes, it is. These nuclear fusions go on all the time inside stars all over the universe. Eventually they end up with atoms containing 26 protons (and a bunch of neutrons). We call that element iron.

So iron is the heaviest element.

No. Iron is the heaviest element created within stars. But after a big star has "burned" all its nuclear fuel and run out of options, it undergoes a final big squeeze and then explodes!

The star explodes?!

Yes. We call it a "nova". During this tremendous explosion, more atoms are slammed together and elements heavier than iron are formed. Like cobalt, mercury and gold!

Wow! When will our sun explode?

Don't worry. This star will not die for billions of more years.

Hey, does this mean that all this "stuff", all these atoms in me are from explosions? From Big Bangs and novas?

That's right. The iron in your blade and in your blood was once at the center of a star, billions of years ago. So was the air we breath and the water we drink.

We are made of star stuff!

You said it. I think that is really amazing, don't you?

Yeah, it sure is!

Why not take a break and think about that? After you've had a rest we'll go into the most important part of Alchemy and atoms.

You know, I think all this stuff about the nucleus is great.
The number of protons defines the element, the neutrons add extra mass, and all the electrons do is balance the charge.

Well, that's an over simplification. Electrons are the part of the atom involved in all the Alchemy!

What?! But the number of protons defines the element. Right?

That's right. The protons define the element because they determine how many electrons are around the nucleus. But the electrons do all the work in Alchemy.

I think I understand what you are saying. The number of electrons around an atom equals the number of protons. So, in a round about way, the proton determines the behavior of the atom by deciding how many electrons it must carry.


Hey, wait a minute. What about ions? They don't have equal numbers of protons and electrons. Do they break the rules? What determines the Alchemy of an ion? The number of electrons or the number of protons?

Good questions. The number of protons defines the element ...

Yes, I know that, but what about the electrons!?

The number of electrons determines the Alchemy. Even ions, with their unbalanced load of electrons, will have a chemistry based on the electrons. BUT, and it's an important "but", the Alchemy of ions is really influenced by the fact that the ions are unnaturally unbalanced.
I'm getting ahead of myself here. We'll come back to that in the next Ancient Element, WATER.

You know, I think an atom is like a beehive.


A beehive. The nucleus of the atom is the hive with a very important queen at its center. All the electrons are like the worker bees which buzz around the hive. They do all the work and they wouldn't be there if it weren't for the queen.

Why, yes. That's a good way to think about it.
Anyway, let's move on. I think you should learn about the electrons with as much detail and determination as you have used for learning about the nucleus. Perhaps more! This next section about electrons isn't easy but it's important to learn ...


Stop that!


I can still hear you.

OK, exactly how do the electrons do all this Alchemy?

Well, the electrons which surround the nucleus of each atom are arranged in very specific ways. Those specific ways determine how the atom will react with other atoms. And that's what Alchemy is all about, isn't it? Atoms reacting with atoms?

Yeah, I suppose. So, I've learned all this stuff about the nucleus of atoms for nothing!

No, no. Goodness no! The nucleus of the atom is very important because it defines the number of electrons and their behavior!

OK, so what's the trick to electrons?

The first "trick" to electrons is to understand electron shells.

Shells?! Like at the beach? Seashells?

No. No. Like egg shells or something like that. Think about layers when you think about electron shells. And think back to what you know about electrons.

Electrons are tiny bits of negative charge which circle the atom.

When you say they "circle the atom" you may be misleading yourself. The electrons are actually whizzing around the atom in patterns that would make a sphere or other three dimensional pattern, not a circle. The rest of this Ancient Element will teach you exactly how they are moving around the nucleus and the shapes their orbits make.

But the first level of understanding electrons is understanding "electron shells"?

Right! We Alchemists like to say electrons move around the atoms in "shells". We often draw those shells to look like circles, but shells don't have a shape. Shells are just an energy level for the electron to sit in. I suppose you can think of them as the size of an atom because the outer most shell determines the atom's size. But not its shape.

What determines the shape?

That would be the orbitals. That's the second level to understanding electrons. But I'm getting ahead of myself. Lets' deal with shells first.
Now tell me, what else do you recall about electrons and protons?

Oh, there has to be equal numbers of electrons and protons, otherwise you have an ion.

Yes. Exactly. So a hydrogen atom must have one electron in its shell, in order to neutralize the proton's positive charge.
Oxygen has 8 protons,...

... so it must have 8 electrons in its shell, or it would be an ion.

Actually, oxygen can't cram 8 electrons into one shell. It splits them up into two different shells.
The first shell, the shell closest to an atom, is called the K-shell.

"K" is for "klose".

No. "K" is for no reason at all, as far as I know. But at least I know how to spell!
Anyway, the K-shell is a small shell and can only hold two electrons. For hydrogen or helium that's all the shell room you need. So hydrogen and helium only have a K-shell.

In other elements, do the rest of the electrons go into bigger shells?

Yes, they do. Just outside the K-shell is the L-shell. It can hold another 8 electrons. So oxygen's six remaining electrons go into the L-shell.
(I'm going to start drawing the nucleus as just a circle with a charge, leaving out all the individual neutrons and protons.)

Hey, if 8 electrons can fit in the L-shell, why don't all 8 of the electrons go there? You know, be all together. Friends! I would. Why don't the electrons?

Because they behave like electrons not like you! Electrons fill shells in a very precise way defined by physics.
Electrons are attracted to the proton by its opposite charge. Opposite charges attract. So two "lucky" electrons get closer to the protons by taking up positions in the K-shell, leaving their "friends" behind.

If electrons are attracted to the proton's positive charge, why don't they go all the way then? Why don't the electrons slam into the protons?

Quantum mechanics.


Not who. What? Quantum mechanics rules the world of the very small. In 1912 a young Danish physicist named Niels Bohr explained that electrons can be in shells (or "orbits") only at well-specified distances from the nucleus. These specific distances are the shells. They are explained by quantum mechanics. Also, the shape of the orbits (orbitals), the number of electrons they can hold, and how the electrons behave, are all explained by the rules of quantum mechanics.

So I must master quantum mechanics to master Alchemy?

No. Not at all. Quantum mechanics sets the rules of chemistry, but you don't need detailed knowledge of quantum mechanics. All you need to understand is that quantum mechanics sets the rules. Know the rules but don't worry about the details from which they came.
It is convenient to imagine the electrons as having certain "likes and dislikes", the way a person likes or dislikes something. But quantum mechanics is the real reason behind electron behavior.

OK. So shells are the first level of electron arrangement to understand.

Right. Shells have to do with the energy of the electrons and they determine the size of an atom, by determining the distance the electrons are from the nucleus.

I see. The electron shells of oxygen are arranged with 2 electrons in the K-shell and 6 in the L-shell. With room for two more.

Yes, exactly. And that "room for two more" is very important, as you will see when we talk about bonding and molecules in the next Ancient Element, WATER. But let's stick with atoms.

Bigger atoms have more shells to juggle more electrons.
Silicon has 14 electrons to arrange in shells, so it has to place the last four into the next largest shell.
Guess what that shell is called.

The M-shell?

Yes. Simple isn't it? As the atoms get bigger we add on more shells to accommodate their electrons and move up the alphabet as we name each new shell.

Until we get to the Z-shell!

Fortunately, atoms don't get so big that we need that many shells.
You should remember that each shell is bigger than the one inside it, so it can hold more electrons.

The K-shell can only hold 2 electrons. The L-shell can only hold 8 electrons. How many can the M-shell hold?

The M-shell can hold up to 18 electrons. The N-shell can hold another 32 electrons.

Wow, that would be a big atom!

Yes, it would be.

I understand these shells. They are easy. We put the electrons into each shell starting with the K-shell and working outward. Any extra electrons keep spilling over into the next higher (larger) shell. Right?

Right. That is good enough for our purposes. It works well for all the small elements and those are the ones that make up most of Alchemy.

What do you mean?

With some of the larger atoms, those with lots of electrons, peculiar things happen with the filling up of the shells. It has to do with some extra complexities about electron behavior.

Does it have to do with those "orbitals" you mentioned earlier? The ones that have to do with the shape of the electron orbits.

Yes, but we don't need to go into that now.

I want to learn about the shapes of atoms. Are atoms round? Like a sphere? Like tiny balls?

Some are and some aren't. It depends on what element that atom is. And it depends on what you call a sphere.

What's that suppose to mean?

Well, it's easy to fall into the habit of imagining atoms as tiny spheres. But atoms are not tiny balls of matter, even though we often think of them that way.
Tell me Arthur, how would you describe the shape of hydrogen or helium atoms?

They are a nucleus with one or two electrons circling it. So I guess they are round like a ball. A sphere. Right?

Sort of right. It is fair to think of the nucleus of an atom as a sphere or a group of spheres (made of protons and neutrons). But atoms are more than a nucleus.

Yeah, they have electrons orbiting around them.

Right. And I'm glad you said "orbiting" instead of "circling" (that time). Even I fall into the habit of saying the "electrons circle the nucleus". That implies the electrons move around the nucleus the way the moon circles the earth.

They don't, do they?

No, they don't. This brings us to the edge of the "magical" world of quantum mechanics.

Ah, oh!

Don't worry. We won't go too deep. The important thing to understand is that an electron orbiting a nucleus is not following a set path around it. Instead it kind of winks in and out of positions all around the nucleus.


Electrons are very small. They are at the very limits of "reality". The world of the very small is dominated by a curious kind of existence based upon statistics and probabilities.

Sounds weird.

It is! There is nothing in our normal (big) world that compares to it.

How does this affect the shape of an atom?

Well, let's define the shape of an atom as the shape of its electrons' orbits. OK?

Fine by me. It makes sense because electrons are outside the nucleus so they should be the part of the atom that determines the shape. Just like they determine its size (with shells).

Good point. Imagine a hydrogen atom with its one electron. How do you think the hydrogen could appear as a sphere?

Well, if the electron moved very quickly around the nucleus it might make it seem like a sphere. But it would have to move up over the top as well as around the edge. Do you see what I mean?

Yes, I do. You are right to point that out. You see, the moon circles the earth along a single plane. Even if it were to move very fast, it would not form a sphere around the earth.

Yeah, it would form a ring or a disk. Not a sphere.

Right. The moon-earth system is shaped like a ring. Not a sphere. But an electron orbiting a nucleus does not form a ring around the nucleus. It makes a sphere. It is a common mistake to think that electrons orbit the nucleus in flat planes. They don't.

I think that's because we are always drawing them that way. It is easier to draw atoms as flat rings than as round spheres. But the electron must move ALL around the nucleus to make a sphere.

Right! And that is exactly what happens around hydrogen. The electron makes a sphere around the proton (and any neutrons) by moving incredibly fast. At any particular moment the electron is in a certain position but it moves so quickly that it is impossible to say "Oh, the electron is right here."

I see. Because, by the time you point to it, it's somewhere else!

Yes! (Also there are other reasons why it is difficult to define the position of an electron but that's an advanced topic.) Therefore, Alchemists picture the electron as being somewhere around the nucleus, but they can't say exactly where.

And it doesn't matter. Because the electron could be anywhere!

Right. BUT there is a certain probability that it is within a certain volume around the nucleus. We call this volume the electron cloud. Here's a drawing of a hydrogen atom's cloud. Each red dot represents the electron at one point in time. It is NOT to mean the atom has hundreds of electrons. It just has one electron that moves so much that it forms a cloud.

I see. Is it this electron cloud which determines the shape of an atom?


And it is always a sphere.


No?! What do you mean "no"?
All the electron shells we looked at were shaped like spheres (even though we drew them as rings).

Remember, those were shells and shells are not meant to represent the shape of the atom. Shells represent the energy levels and size (radius) of an atom.
The time has come to introduce the idea of subshells, which are also called "orbitals". They cause shape. Bohr thought all atoms had sphere-shaped electron clouds, like hydrogen. He was wrong. He didn't know about subshells.

Subshells? Are they like shells? Are they like the K-shell and L-shell and M-shell and others?

No. Those shells are the principle shells. Those principle shells have subshells to them. Subshells are a detail of shells.

Sounds like we are going into more detail here.

We are, so pay attention. The shells (K, L, M and so on) are a convenient way to imagine electron clouds. They define how far away the electrons (in that shell) are from the nucleus.
Shells have to do with atomic RADIUS.
But when you start to look at shells in detail you learn they are made of subshells which we call "orbitals".
Orbitals define the true SHAPE of the electron cloud and thus the true shape of atoms.

OK, let me see if I got this straight.
Shells, like K, L, M and so on, define how far away from the nucleus the electrons orbit.
And subshells or orbitals define the shape of those orbits.


And those orbitals may or may not be spheres?

There are 4 basic subshells, or orbitals, each with a specific shape - s orbitals, p orbitals, d orbitals and f orbitals. The easiest subshell to understand is the s orbital. Electrons in an s orbital are a specific distance from the nucleus (determined by the shell), but can be in any direction around it.

What's that mean.

It means that electrons in s orbitals form an electron cloud shaped like a sphere.

That's easy! S orbitals are spheres.

Right. Their electrons are likely to be found in any direction from the nucleus (that's a characteristic of an s orbital) so that makes a sphere. Those electrons are at a certain distance from the nucleus (that's a characteristic of their shell).
Hydrogen and helium have only s orbitals, so hydrogen and helium are simple spheres. The fact that they have only K-shells means they are (roughly) the same size.

Aren't they the only elements with K-shells as their outer (only) shell?

That's right. As a matter of fact, K-shells can ONLY have s orbitals.

That means most of the atoms in the universe (hydrogens and heliums) have electrons orbiting them in simple spheres. That's easy. What about bigger atoms, with L-shells. Do they only have s orbitals too?

Yes. In fact, ALL shells have s orbitals.
L-shells have s orbitals and they also can have p orbitals.

What's a p orbital?

P orbitals are shaped like a pair of lobes. Like a figure 8. But not a flat figure 8. It's like a figure 8 that has been spun in the 3rd dimension (out of the page).

Huh? What do you mean?

OK, lets' back up a wee bit. Imagine the letter O, written on a page. It has the shape of a plate, a disk. But the s orbital is NOT a disk, it is a sphere. You can imagine that the "O" is spun in the 3rd dimension (out of the page) to make the sphere.

Yeah, I understand that much.

Good. To understand the shape of p orbitals, imagine the figure 8 is spun the same way (along its long axis). It makes a pair of lobes.

No it doesn't. It makes a doughnut!

If you think it's making a doughnut shape you are imagining it spinning along the short axis, not the long axis.


OK, try this. Imagine the figure 8 to be dangling from a string. If you give it a spin, it will look like a fat figure 8 made of two lobes. One lobe at the top and another at the bottom.

Oh, I see. It would make a pair of spheres stuck together.

Right. The center of the figure 8 is at the center of the atom. At the nucleus.

So the lobes look like a pair of rounded wings sticking out of the atom?

Aye. The p orbitals are more complex than s orbitals because they can have three different orientations. That means there can be up to three different types of p orbitals.

This sounds like a third, deeper level of electron detail.

It is!

What is it? "Orientations"? What's that all about?

What I mean is the figure 8 could be positioned in any one of the three dimensions.

What are the three dimensions?

Well, some people think of the three dimensions as "height, length and width". That's pretty good, but we Alchemists (and other scientists) call them "x, y and z". It has to do with a form of math called geometry.

Ugh. Not math!

Don't worry about it. Just imagine three different figure 8 lobes lined up in the three directions. One lies up and down (like the 8), another points sideways (left and right) and the third points in and out of your book.

I can see why you don't have any p orbitals in atoms with only a K-shell. It looks like these p orbitals need more room.

Well, actually it has to do with quantum mechanics. But your guess is pretty close to the truth and good enough for our class. The smallest atoms have only a K-shell so all they can have is a simple s orbital. A sphere. But bigger atoms can also have p orbitals.

Did you say there were four kinds of orbitals?

Yes. All together there are four kinds of orbitals - s, p, d and f.

What are the d and f orbitals shaped like? How many are there (of each)? What kinds of atoms have d or f orbitals?

My, my you ARE an inquisitive lad. There are 5 different types of d orbitals and 7 different types of f orbitals. Each type is a complex mix of spheres, lobes, rings and other strange shapes. They make the p orbitals look easy!

Oh, no! Do I have to learn about them?

Not from me. Not in this class. Fortunately, those complex orbitals are only found in certain metals. Only advanced Alchemists bother to learn about d and f orbitals. Most of the elements you are likely to work with have only s and p orbitals. Or combinations of s and p orbitals.

Great. So exactly how does an atom pack these orbitals in. Is it like filling shells?

Yes, it is. Let's take oxygen as an example. First, remind me how the electrons are arranged in oxygen's shells.

Easy. The inner shell in all atoms is the K-shell and it can only hold two electrons. Does that mean that even oxygen's K-shell is just an s orbital?

Yes! That's right. All atoms have K-shells, so all atoms have a sphere (s orbital) as the inner most orbital. But it's the orbitals in the OUTER shell that give an atom its shape.

I know. Let's see, there are 6 more electrons for oxygen and they all go into the L-shell. You said the L-shell can have both s and p orbitals. Right?

That's right. And this is where many Alchemy students get confused. Remember, there are TWO groups of orbitals in the L-shell. There is one s orbital (only one type) and one group of p orbitals (of three types: x, y or z).

Hmm, this IS complex. How do I put the 6 remaining electrons into them?

Well, the electrons are distributed from the lowest to the highest energies.
All elements fill their s orbitals before they fill their p orbitals because s orbitals are lower in energy than p orbitals. It's another law. It's just like filling the K-shell before moving on to fill the L-shell. But here we are talking about orbitals. S orbitals are of lower energy than p orbitals so they get filled first.

OK. So I should put all 6 electrons into the s orbital of oxygen's L-shell.

No, that would be wrong. But you wouldn't have known that until you learned about Pauli's exclusion principle.

What's that?

Pauli's exclusion principle tells us that no more than two electrons may occupy a single orbital. (Pauli's exclusion principle also says something else, but we'll leave that for later.)

Only two electrons per orbital. I bet this law is due to some powerful force called quantum mechanics.

Aye. Quantum mechanics determines all these rules about the way electrons behave. With the K-shell, you only had a single orbital, so both electrons fit in it without difficulty. But now we have more electrons to juggle in the L-shell.

So, if I understand you, oxygen's 8 electrons are distributed in a more complex way than we have been imagining it.

Yes. We are getting into the details of atomic structure. It's called "electron configuration".
The K-shell can only hold two electrons because it has only an s orbital.
The other 6 electrons that go into oxygen's L-shell are distributed among the s and p orbitals. And remember, there are three different types of p orbitals - x, y and z.

Oh, no! This is getting hard.

Now, come on Arthur! Don't let that get you down. You learned how to fill shells in a specific order. All you are learning now is how to fill the orbitals in specific order. Now tell me how you would distribute the remaining 6 electrons in oxygen's L-shell. Remember, the s orbital is of lower energy than the p orbitals so it will get filled first.

And Pauli says each orbital gets only two electrons. Hmmm.
OK, 2 of the electrons go into the s orbital of the L-shell. Right?

Right. That takes care of 4 of oxygen's electrons. Two are in the K-shell (which only has a single s orbital) and two more are in the s orbital of the L-shell.
And that reminds me of an interesting point worth repeating. Because there is only one type of s orbital and orbitals can only hold two electrons, that means all s orbitals can only hold 2 electrons. And all shells start with an s orbital (as the lowest energy of the shell).

Are you trying to confuse me on purpose?

No, sorry if I have. What I am trying to point out is that the s orbitals are found in all shells - K, L, M, and so on. But the s orbitals are only of one type. You can only have one type of sphere. There is no other kind.

Yeah, I suppose. What's your point?

My point is that p orbitals, which are of higher energy than s orbitals, are in THREE types (x, y, and z). So p orbitals are where you spend most of your time figuring out the patterns. P orbitals are more complex than s orbitals.

They sure are! I like S orbitals. S orbitals are found in all shells (K, L, M and so on) and can hold only two electrons because s orbitals are only of one type.

Right. Now let's get back to the oxygen problem. You have 2 electrons in its K-shell (s orbital) and 2 electrons in the L-shell's s orbital. That leaves you with four electrons remaining.

They must go into the p orbitals of the L-shell. I guess I could put them into any one of the x, y or z types. Is that right?

Sort of right. This brings us to another rule about electron distribution.
Hund's rule says that when more than one orbital is available for occupation, electrons occupy separate orbitals first. (Hund's rule also says something else, but we'll leave that for later.)


So, assign one electron to each p orbital.

OK. I put one electron in the x type, one in the y type and another electron in the z type. But I'm left with one electron. Where does it go?

It goes into which ever p orbital you want to put it.

What do you mean?

Well, you might think to put one electron in the x type and one in the y type and the other two in the z type.

Yeah, that would work. That would put no more than two electrons per orbital (type). Pauli would be pleased. But is Hund happy?

Of course he's happy. Think about it. All Hund says is that you must first put an electron into each orbital (of the same energy level, of the same shape). Once all the orbitals (of the same energy level of that shape) have an electron, you can start placing the other electrons into orbitals to create orbital electron pairs.

OK. That means I could end up with two electrons in the x-p orbital and have one in the y-p orbital and one in the z-p orbital. That would work too!

Right. It doesn't matter which p orbital (x, y or z) ends up with a pair of electrons. All that matters is that first all the p orbitals get an electron. The first three electrons will go into the three p orbitals, one in each.

So it would be wrong to put two in the x-p orbital and two in the y-p orbital, because that leaves none for the z-p orbital. Is that right? That's wrong?

Yes, that's wrong. Pauli would be pleased (because there's no more than two electrons per orbital) but Hund would not be happy (because Hund wants all the orbitals of the same energy to get an electron before doubling them up in pairs).

Wow, this electron stuff is hard. It's hard to please everyone's rules!

Yes, I agree. But these rules are the rules of quantum mechanics.
You could have ended up with two electrons into the z-p orbital and one electron each into the x-p and y-p orbitals. That would have been correct too. It's all the same. It doesn't matter because all the p orbitals in the same shell have the same energy.

Let me see if I got this.
An oxygen atom has two electrons in its K-shell and 6 electrons in its L-shell. That is nothing new.
The two electrons in the K-shell are in a simple s orbital, a sphere.
The remaining 6 electrons in the L-shell are distributed among the s and p orbitals. Of those 6 electrons, 2 go into the s orbital of the L-shell and the remaining four go into any of the three types of p orbitals.

Right. The s orbital is the lowest energy orbital of any shell, so it is the first to be filled. Once you have two electrons in it, you must move up to the three p orbitals to distribute the rest.

But they must go into each p orbital one at a time. (That's Hund's rule.)

Right. That's because all three of the p orbitals are of the same energy. They are identical, so we use Hund's rule to distribute electrons among orbitals of the same energy. The three p orbitals (x-p, y-p and z-p) are identical in energy (they are only different in orientation).

Once each p orbital has an electron, any remaining electrons can go into each p orbital to make a pair in each orbital, but you can't have more than two electrons in each orbital. (That's Pauli's exclusion principle.)

Correct! We could summarize the orbitals of an oxygen atom by writing it down like this.
Oxygen's K-shell (s2)
Oxygen's L-shell (s2, x-p2, y-p1, z-p1)

I like that. It looks nicer than saying it all. It makes it much clearer and helps me see where all the electrons go. That way I can keep track of all these rules.

Yes, I agree. There are other ways to write the same thing. But this way is a good way. Regardless of how you write it, you should understand how you figure it out!
Just remember to:
1) fill all shells first, starting with the lowest energy shell (K) and working outward (L, M, etc.).
2) then re-assign electrons starting with the lowest energy orbital (s orbital) and then moving up to the higher energy orbitals (the p orbitals).

And the p orbitals can be in any of the three types - x, y and z. You have to place an electron in all three of the p orbitals before you start to double up the electrons into pairs. Hund says so.

Now remember, the reason we went through all this hard work is we wanted to know the SHAPE of the oxygen atom.

OH, yeah! It's the shape of the outer orbitals which give an atom its final shape, right?

Right, you are. You can ignore oxygen's s orbital in the K-shell. It's hidden underneath the L-shell. In order to "see" the shape of the oxygen, you must overlap the shapes of all its L-shell orbitals.


Just line them up and overlap them. Remember, the nucleus is at the center of ALL orbitals, so you can imagine laying one electron cloud from each orbital over the nucleus. When all the outer shell orbitals are overlapped, you get the complete shape of the atom!

I think I see what you mean.
I also see that the x-p orbital is full so it is twice as thick as the other two.

Right, and that's an important point. Just because an orbital is only half-full, that DOESN'T mean the electron stays in just one lobe. It moves between the two lobes equally. Half-full orbitals are just less dense.

I get it. When I overlap all of oxygen's L-shell orbitals I see a thick sphere in the center (the s orbital), a thick pair of lobes (the full x-p orbital) and another two pairs of lobes which are less thick. They are at right angles to the thick one.

Yes, you've got it. Naturally it's hard to draw it well in only two dimensions, but I think you can imagine its shape.

The oxygen atom has a much more complex shape than the hydrogen atom!

Yes. It's those p orbitals. They really spice things up.
Remember, I could have ended up with that electron pair in a different p orbital and it would still have been correct. Why not write that for me? Show me how to write the electron structure of oxygen with the electron pair in a different orbital.

Oxygen's K-shell (s2)
Oxygen's L-shell (s2, x-p1, y-p2, z-p1)
Here I've ended up with the pair in the y-p orbital. The important thing is that Hund is happy (because first I filled all the p orbitals before assigning the last electron to any old p orbital) and Pauli is pleased (because there are no more than two electrons in each orbital).

Correct. Notice that the atom will still have the same shape, it will just be in a different orientation.
All atoms work that way. But there's two things I want to point out.
First, in some of the large metal atoms, the d and f orbitals must be included in the puzzle. Their orbitals are in odd shapes and there are more types of them (5 of the d types and 7 of the f types).
Second, in some larger atoms (with lots of electrons) the energy levels of the orbitals from different shells start to overlap. That causes some electrons to be in a larger shell and in a different orbital than you might expect.

What!!? Are there any real "rules" in Alchemy?

Yes, there are. Even these "exceptions" can be understood if we went into the details of assigning electrons to their orbitals. But in this course, at this level of your education, I want to stick to small atoms and simple rules.

You call these simple!?

Well, they are understandable. The complexities I want to avoid here, have to do with the details of electron energy levels in big atoms.
Regardless, ALL orbitals must obey Pauli's exclusion principle and Hund's rule. Even the d and f orbitals. Even the big atoms.

We aren't going to do those other orbitals because they are too hard, right?

Well, they aren't really all that hard. They follow the same rules. But their shapes are hard to imagine and I'd have to teach you a more difficult way to figure out how the energy levels of each atom are determined. You see, the bigger shells have d and f orbitals, but they don't like to use them. That causes electrons to skip up to higher shells and I don't want to go into that here.

Uggh! Sounds complex. Let's not do that.

We won't. Besides, you won't miss much by not doing them. Maybe some other day.


However, it is important to understand the s and p orbitals, so let's do another atom.

Aw! Let's not.

Arthur! I'm surprised at you.

Hey, these are hard! And I'm confused.

That's all the more reason to practice on another element. I'll help you as you go.
Try to figure out the electron structure of carbon.

How many electrons does it have?

Well, it has 6 protons ...

So it must have 6 electrons. (Otherwise it would be an ion.)
Hey, this will be easy. It's less electrons than oxygen!
OK, 2 electrons go into the K-shell and the remaining 4 go into the L-shell.

Right. Always start with the shells. The shells are the principle electron configuration and they help you figure out the size of the atom's electron cloud, but they don't tell you the shape.

I know! That's why I then go on to the subshells called orbitals.
The K-shell has an s orbital (that's all it can have) and two electrons go into it.
Carbon's K-shell is (s2)
That leaves the L-shell. I have 4 electrons to distribute among the L-shell's one s orbital and three p orbitals. Right?


I have to use Hund's rule and first place one electron into each orbital.
So carbon's L-shell is (s1, x-p1, y-p1, z-p1).
There! All the electrons are assigned.

Nope. You got it wrong.

What!? Hund is happy and so is Pauli!

Calm down. You've made a common error. Remember that s orbitals are of lower energy than p orbitals. So the s orbital gets filled first. Filled completely with both electrons.

Oh, right. I forgot that s orbitals are not really the same energy as p orbitals. That's kind of tricky because they are both in the same L-shell and I thought the shells have to do with energy.

They do. And you're right, it is tricky. The difference in energy between an s and a p orbital is very small. Much smaller than the difference in energy between a K-shell and an L-shell. But there is a difference. S orbitals are of slightly lower energy than p orbitals, so they are filled first, completely, with two electrons.

OK. That means carbon's L-shell has a full s orbital (s2) and the remaining two electrons go into the three p orbitals. Hey, how can I put two electrons into three orbitals? What do I do?

What do you think you should do? Remember, all you have to worry about is Hund's rule.

Well, I could put one electron in the x-p orbital and one in the y-p orbital, but that means there would be none in the z-p orbital.

Is that a problem? Are you breaking any rules by leaving an orbital empty?

No, but it doesn't feel right.

It may feel wrong, but it is right! There's nothing wrong with leaving an orbital empty if that's the only way to finish the atom. So tell me, what's the electronic configuration of carbon?

Carbon's K-shell has a full s orbital (s2) and its L-shell has a full s orbital (s2) along with two p orbitals which are half full. They could be (x-p1, y-p1, z-p0).

That's right, although we usually don't bother writing the empty orbital. Any good Alchemist would know it should be there and know that it is empty.

But I feel really uncomfortable with this. Which p orbital should I leave empty, they x-p, y-p or z-p? Does it matter?

Did it matter with the oxygen's p orbitals which one got the pair?

No. They are all the same.
Oh! I see. It doesn't matter which one I leave empty because you really can't tell them apart anyway. All the p orbitals have the same energy.


So there's three different ways to assign the last electrons in carbon's p orbitals.
They could be (x-p1, y-p1) which leaves the z-p orbital empty,
or (y-p1, z-p1) which leaves the x-p orbital empty,
or (x-p1, z-p1) which leaves the y-p orbital empty.

Right. They are all right. All three ways of assigning them are right for two reasons. First, we can't tell the three orbitals apart, and second, the electrons can't tell them apart either! As a matter of fact the two electrons in the p orbitals of carbon's L-shell probably move all around to form all three possibilities.

Really? How's that?

Well, the two electrons in the p orbitals have the exact same energy so they can end up in any one of the three orbitals at any one time. The only thing they can't do is ...

I know! I know! They can't end up in the same orbital at the same time because that goes against Hund's rule!

Right you are! You can't have an orbital with a (x-p2), (y-p2) or (z-p2) because that would disobey Hund's rule.

Even though Pauli's exclusion principle would not be broken.

Right! Now, can you imagine the final shape of a carbon atom?

Well, its shaped by its L-shell, because that's carbon's outer shell.
Hmmm. I imagine it as a thick sphere (the L-shell's full s orbital) with two sets of thin lobes at right angles to each other.

Right again. One of the p orbitals is missing, so the carbon atom is kind of flat looking.
I won't bother drawing it because you should try to imagine them yourself. We can only draw in two dimensions but we can think in all three dimensions, so it's good to practice using your imagination to "see" the shapes of atoms.

This is pretty hard stuff. I'm going to read over all this electron configuration stuff again and go through it real slow while I jot down the important bits. And I'll use that way of writing it to make it clear. And I'll practice using my imagination to "see" the atom shapes.

That's an excellent idea.
Nobody understands how to assign electrons to orbitals the first time they see it. You have to go through it a few times and practice it. Think of these as puzzles to be solved rather than simply questions to be answered.

Puzzles are much more fun than questions.

Yes, I agree.
It's also a good idea to exercise your "visual imagination". Some people think that only artist use their "mind's eye", but Alchemists do it all the time.

Sounds like fun!

It is.
Any questions?

Yeah, but I think I might regret it. You said something about Pauli's exclusion principle and Hund's rule that made me think there was one final layer of complexity. You said they say something else but you'd talk about it later.

Oh, yes! Spin.

Spin? Electrons spin?

Yes. Sort of. All electrons have a final property that I forgot to mention called spin. It is the last part of quantum mechanics, but it ties in to all the rules.

Is it hard?

Not really. Not as hard as this other stuff.

OK, let's hear it!

Spin isn't like the spin of a top, but some Alchemists like to think of it that way. Spin is the way an electron can "be". Rather than go into the details, let's accept that an electron can be in two different states.

Like "up" and "down" or "left" and "right"?

Yes. It doesn't matter what you want to call them. Just so long as you know that they are opposites of each other.

What do Alchemists call them?

Unfortunately, some Alchemists call them +1/2 and -1/2. But they have nothing to do with their charge. (Remember all electrons are -1 in charge.)

Then why did they choose to call them +1/2 and -1/2?

Because they are defined by a "wave function" in math and I won't go into it at all. It requires a great deal of math called trigonometry. All you need to know about spin is that there are two types and they are opposite to each other. Most Alchemist prefer to call them "up" or "down". I like that because it avoids that confusing half numbers of trigonometry.

Fine. What is spin used for?

It helps refine our understanding of electron configurations and helps explain some pretty advanced Alchemy involving weird bonds, magnetism and stuff like that. But that's far too advanced for us here.

OK, but how does it fit in with Pauli and Hund?

Oh, that. Well, Hund's complete rule is that when more than one orbital is available for occupation, electrons occupy separate orbitals ...

Yes, I know that

... and do so with parallel spins.

OK, I didn't know that.

There's little reason why you would have to know that for a course at this level. But you asked!

Does this spin rule of Hund's mean that the electrons in carbon's two half-full p orbitals are both "parallel"?

Yes, that's exactly what Hund's rule would say.

So they are both "up" or both "down" but you wouldn't have one "up" and the other "down".

That's right!

Hmmm. I wonder what that means for the four electrons in oxygen's p orbitals. Remember them? Oxygen's L-shell p orbitals had two electrons in one p orbital (any p orbital, it doesn't matter) and single electrons in the other two p orbitals. How does spin fit into that?

You tell me. Think about Hund's rule, now with his spin rule.

OK, the first three electrons would go one each into the three p orbitals. Hund's rule says they will all be parallel. All "up" or all "down". Right?

Absolutely right. What about that last electron? It has to pair up with one of the three. What do you think its spin will be?

I don't know. Hund's rule is no help. Maybe that last electron will have the same spin as all the others.

That's a good guess, but the wrong one. You wouldn't have know that. You see Pauli's exclusion principle says that no more than two electrons can occupy a single orbital ...

Yeah, I know that.

... and if two electrons do occupy a single orbital, their spins must be opposite.

OK, I didn't know that.
So oxygen's L-shell p orbitals will have one full orbital (any one of the three) with one electron "up" and the other electron "down" while the other two orbitals will have only one electron in each but those electrons will match in their spin.

Yes! Exactly! And congratulations are in order here.
Arthur, you now understand the most important details of atomic structure AND quantum mechanics!

All I understand (I think) is what's in a nucleus and where electrons go.

That's right!
Very advanced Alchemists will understand quantum mechanics using math instead of they way we've done it, but all this talk about electrons has taught you all four levels of quantum mechanics.

Huh? I think I might have missed that.

OK, let me explain.
The first level of quantum mechanics are the shells. K-shells, L-shells, etc. are the first quantum level.

OK, what's the second?

That would be the subshells or orbitals. You know all four kinds of orbitals: s, p, d and f orbitals.

Yeah, although I don't know much about the d and f orbitals except that they come in five types of d's and 7 types of f's.

True, but that's all you really need to know (for most Alchemy). And those "types" of orbitals are the third level of quantum mechanics. The third level of quantum mechanics involves the orientation of the orbitals. You know that there is only one kind of s orbital and it's shaped like a sphere

Yeah, and there are three types of p orbitals, all shaped like lobes, one for each dimension. And all I know about the d and f orbital shapes is that they are complex lobes and doughnut shapes.

Right. That's all there is to the third level of quantum mechanics!

So the last level of quantum mechanics is the spin, and there's only two ways for an electron to be, either "up" or "down".

Right! That's the four levels of quantum mechanics.

I think the second and third levels are kind of mixed together.

Well, yeah they are. I want to avoid the math that separates them.

That's fine by me! I understand now how all four quantum levels define an electron.

That's right. When you know all four quantum levels of an electron, you know everything about its home in an atom. You know what shell it's in, you know its orbital shape and type, and you know its spin.

So the four quantum values are really an address for every electron.

That's right! No two electrons can have the exact same values in an atom. That's really what Pauli's exclusion principle is all about.

I think I see. So two electrons may have the same shell (say an L-shell), share the same orbital shape (say a p orbital) and even the same orientation (x-p orbital, for example), but they would have to have different spins.

Right. That is the most important law in quantum mechanics. Pauli says no two electrons can have the same four quantum values. They are excluded from sharing the same values. That's why it's called Pauli's exclusion principle!

I see. I think.

Good. Pauli and Hund would be proud. And so am I! You've learned a lot of difficult material here.

Well, I don't know if I fully understand it all but I'll review it again,

Good idea. As you review your electron configurations, think about Pauli's exclusion principle as well as Hund's rule. Once you feel comfortable with all this, read through your notes and then go through the Questions and Answers. Remember, some of the Questions are very hard and teach you new things. So don't feel bad if you don't get every answer right. Just be sure you understand the answers I give for them. Enjoy them as puzzles, OK?


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In this sample, only the first Ancient Element (AIR) is available. The other Elements, WATER, EARTH and FIRE, are included in the complete hypertextbook, and each of those Elements are about twice as long as AIR. To learn more about the course and hypertextbook, visit the Principles of Alchemy (Chemistry) website.