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Nuclear Chemistry
Radioactivity
Stability of Binding Nulcei Page [1 of 2]
So, nuclei decay, but not all of them decay. Only some of them decay. Can we, at least qualitatively or semiquantitatively talk about why some nuclei decay and some don’t? Take a look at the graphic. The graphic shows the
stable nuclei that there are in the universe – or at least in our known universe – where we plotted the number of
neutrons on the y-axis and the number of protons on the x-axis. And the stable nuclei, those that don’t undergo
radioactive decay, are indicated in black. And then the ones that do undergo radioactive decay are indicated in
orange.
And one of the first things that you’ll notice is that the data, for the most part, fall above the line of one neutron per
proton. Another way to say that is that, except for hydrogen 1, just a plain old proton, and helium-3, which is 1 proton
and 2 neutrons, all are stable nuclei – have 1 or more neutrons for each proton. That’s to say here we have our
nucleus, and we can’t take a bunch of just positively charged things – just protons – and jam them all together and
expect the nucleus to be stable. What we have to do is throw some neutrons in there to sort of dilute it out so that the
nucleus is going to be stable. And if we don’t have at least one neutron for every proton, that nucleus is not going to
be stable, except for these first couple. And in general, as you go further and further along – as you add more and
more protons – you need a higher fraction of neutrons in order to get a stable nucleus.
Now the other thing that you’ll note is that at atomic number 84 and above, all the nuclei are radioactive. So when you
get a nucleus that’s just so big that it’s got 84 protons and some huge number of neutrons, those nuclei are just so big
now that they’re going to want to do something else. They want to be something else and we’ll talk about why they
want to be something else in the next tutorial. But let’s at least qualitatively talk about why we have some that are
stable. And the first thing to note is that there’s such a thing as a magic number, or a series of magic numbers.
These are empirical, but they do suggest a theory that I’ll talk about in a second. First let me point out the trend.
Nuclei with 2 protons, 8 protons, 20 protons, 28 protons, 50 protons or 82 protons and nuclei with 2, 8, 20, 28, 50, 82
and 126 neutrons are generally more stable. In other words, a greater fraction of the black dots have these magic
numbers then might be predicted, based on no special numbers. And, in particular, 2, 8, 20, 28, 50 and 82
correspond to helium, oxygen, calcium, nickel, tin and lead – and we’re going to come back to lead later on and you’ll
see that lead has a particular specialness about it.
Okay, so why magic numbers? Why are these numbers appearing over and over again? For instance, a lot of these
have more isotopes than they might have expected. In other words, calcium has a lot of isotopes and it’s because
there’s special stability associated with 20 protons. Now why? Well, just as there are shells for electrons – electron
shells and filled shells, like noble gas configurations – there appears to be a shell structure to the nucleon count. And
so, when you have 2 neutrons and 2 protons – that’s a double magic number – that’s the helium nucleus, and the
helium nucleus is certainly very stable. And so by at least hypothesizing this shell structure, we can explain why some
nuclei seem to be more stable than others.
But something else that’s true, in a more general sense, is that nuclei with even numbers of proton and even numbers
of neutron come up more often as stable nuclei than those nuclei that have odd numbers of protons and odd numbers
of neutrons. And to show you the statistics on that, of the isotopes in that particular figure, 157 of them that are stable
have an even numbers of protons and even numbers of neutrons. 53 have even numbers of protons and odd
numbers of neutrons. 50 have odd numbers of protons and even numbers of neutrons. And only 5 have both an odd
number of protons and an odd number of neutrons.
Now, it’s not to say that the odd odds are unstable. For instance, one of the most stable, important elements – one of
them that takes up almost 80 percent of air – is nitrogen. And the most stable isotope of nitrogen is nitrogen-14,
which is an odd/odd. It has 7 protons and 7 neutrons. So this is a statistical look, and it seems to suggest that in this
shell model, where we get the magic numbers, that there is a better situation when we have even numbers of protons
and even numbers of neutrons, suggests that they like to be paired up.
So here’s a little piece of that table. Again, in the graphic – where we have numbers of neutrons along the y-axis,
number of protons along the x-axis – I wanted to point out how it works to predict when a nucleus ought to go
radioactive decay and which way it ought to go. For instance, lets look at carbon-14. Carbon-14 has 6 protons and 8
neutrons. It’s the element that is used in radiocarbon dating that we’ll talk about later on. And if it were going to make
a move to become a stable nucleon – right now it’s a red dot, which means that it’s an unstable nucleon – what’s it
going to do? Well, it’s going to move either along the diagonal via beta emission, moving diagonally downward, or
Nuclear Chemistry
Radioactivity
Stability of Binding Nulcei Page [2 of 2]
along the diagonal diagonally upward, because both beta emission and positron emission – or electron capture – turn
either protons into neutrons or neutrons into protons. And those are going to be movements on the 45-degree
diagonal. So in particular, carbon-14, to become a stable nucleus, is going to beta emit and become nitrogen-14. So
from here to here, one jump means beta emission and so carbon-14 turns into nitrogen-14.
Let’s look at another one. Let’s look at carbon-11. I’ll tell you that it’s a positron emitter used for positron emission
tomography. So let’s go to carbon-11, which is this spot right here. And now, what do we want to do? Well, we want
to move on a 45-degree angle but northwest to here, which is boron-11. So carbon-11 becomes boron-11 and it goes
from being something radioactive to something that’s stable and the way it gets there is positron emission. So again,
all the black spots, those are the stable isotopes and the orange-red spots are the radioactive isotopes.
Now, if you go way up into the upper right-hand corner of the graphic, you’ll see that there are a bunch of nuclei that
become really unstable. So 84 and above, they’re all unstable. And if you want to make a general statement, the
nuclei that are up in the upper right-hand corner will want to alpha decay. By alpha decaying, they will decrease the
number of protons and they will decrease the number of neutrons. You don’t see alpha decay among the light
elements. You’ll only see alpha decay among the very heavy elements.
Now, in general, a heavy element is not going to be able to undergo a single nuclear decay process and get to a
stable element. It’s gong to undergo a chain of decays. And if you take a look at the graphic now, you’ll see the chain
of decays that take uranium-238, which is the predominant isotope of uranium-238, all the way down into, ultimately, a
stable isotope. And it goes through a series of alpha and beta decays. So the first step is an alpha decay to thorium234 and then beta decay to protactinium and then a beta decay to uranium-234 and then an alpha decay to thorium230. Remember alpha decays involve decreases the mass number of 4. Beta decays involve no change in the mass
number. It’s change in the identity of the element by changing the number of neutrons to protons. And then thorium230 alpha decays to radium-226 which alpha decays to radon-222. Radon-222 is the thing that collects in your
basement. So that’s how the most common isotope of uranium – uranium-238 – gets to radon-222, which collects in
your basements. Radon decays to polonium-218. Polonium-218 alpha decays to lead 214 and then lead beta decays
to bismuth-214. And you can just follow all of these decays all the way on down. Bismuth-214 beta decays to
polonium-214 which alpha decays to lead-210. Lead, remember, has 82 protons so that’s a magic number, and so I
would guess that lead-210, if it is radioactive, it probably has a relatively long half-life or it has relatively greater
stability. But in fact, lead-210 beta decays to bismuth-210 which beta decays to polonium-21 which alpha decays to
lead-206. And lead-206 has 82 protons. It has 206 total nucleons and it is stable.
So by a very circuitous path involving a series of alpha decays and beta decays, we get from uranium-238 all the way
to lead-206. And finally, we hit a point that is stable on the plot of total numbers of neutrons to the number of protons.
So this is a relatively qualitative treatment. What we’re going to see next is a quantitative treatment that tells us why
some nuclei are going to be more stable than others and what it involves, it’s sort of what’s the energy of the nucleus?
How much energy does the nucleus have and how much energy does it take to break the nucleus apart. Remember,
we’re talking about reactions of the nucleus. And so we, up until now, haven’t really talked about the energy of the
nucleus. In the way that we talk about energy of chemical reactions, what we need to do is talk about the energy of
nuclear reactions.