The Alpha Particle : Part 3 : Binding Energy

The Field Guide to Particle Physics
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The definitive resource for all data in particle physics is the Particle Data Group: https://pdg.lbl.gov.

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A few References and Resources for you.

Isotopes of Helium:
https://en.wikipedia.org/wiki/Isotopes_of_helium

Helium Fact Sheet from NIST:
https://webbook.nist.gov/cgi/inchi/InChI%3D1S/He

We've got fun details about Protons, Neutrons and the atomic nucleus on our Field Guide website.

Some helpful links to ideas about nuclear binding energy:
http://hyperphysics.phy-astr.gsu.edu/hbase/NucEne/nucbin.html
https://en.wikipedia.org/wiki/Nuclear_binding_energy
... and that famous plot.

The Alpha Particle
Part 3 - Binding Energy

At this point you might be wondering. This is all great, but helium is a chemical element. It’s a gas. What on Earth does helium have to do with particle physics?!

We’re almost there. And when you see the connection, you might freak out. But let’s briefly review what we know so far.

Helium is a gas trapped underground and made up of Helium atoms. Each atom has a nucleus with two protons. Almost all of the helium on Earth also has two neutrons.

The chemistry of Helium is rather boring. Helium is a noble gas. It doesn’t usually form chemical bonds .The nuclear physics of Helium by comparison, is fascinating. So let’s talk about some nuclear physics.

Chemistry vs Nuclear Physics

Part of what makes Chemistry so hard to understand is the diversity of the elements. With almost 100 possibilities, the number of combinations of elements - the number of molecules - is effectively limitless. Nuclear physics, by contrast, includes only protons and neutrons.

Doesn’t that feel a little more manageable?

The nuclei of atoms are considerably easier to wrap your mind around. They’re super tiny globs, made up of only protons and neutrons, bound together into a ball. That’s it.

Admittedly, it is weird that nuclei are so small compared to the rest of the atom. And it is weird that almost all of the atomic mass sits inside the nucleus. But at least it’s organized neatly.

Of course, the insides of those individual protons and neutrons is horribly complicated. Those particles are sloppy bags of subatomic goo that are extremely difficult to describe mathematically. Because all that madness is neatly organized in those tiny packages - those protons and neutrons - we won’t worry about it here.  But we will say that all that crazy internal subnuclear goo leaves a residual “stickiness” around the edges of the particles.

That residual stickiness is still pretty powerful. Pulling apart a chemical bond might cost something like 5 electron Volts of Energy - or less! Want to pull a proton off a Helium atom? That’ll cost you almost two million times as much energy.

And that’s a good thing. The nucleus only has positive electric charge. It’s just protons and neutrons. If those nuclear bonds - that nuclear stickiness - weren’t so strong, they might just blow apart!

The nuclear force, is seams, it’s much, much stronger than the electrical force. Nuclear physics might seem simpler to describe at first, but it is a VERY different kind of physics.

Binding Energy

It’s not really possible to go in and just pull a proton out of a nucleus. But thinking about doing that - and thinking about how much energy is required - is a good proxy for thinking about how tightly bound the nucleus is.

Those protons and neutrons like to be bound together. Especially those neutrons.

We call the typical amount of energy it takes to pull one of those particles off the nucleus, the binding energy.

If you lined up all the different nuclei by size, you’d see a stark contrast in binding energy.

On the small side, you’d see things like hydrogen: A single proton with one or two neutrons. You’d also find Helium-3 and Helium-4. Lithium and so on. Their typical binding energy is pretty small, relatively speaking.

On the large side you’d see bismuth and uranium. Thorium and all their various isotopes. They’re binding energy is pretty strong.

The generic trend is that nuclei become more tightly bound with more and more particles. It happens pretty rapidly, with Carbon - having only 6 protons - having eight times the binding energy of the smallest nucleus.

That rapid growth in binding energy levels off soon enough, so that atoms like Iron-56 enjoy some of the most tightly bound nuclei around. At that point the nucleus becomes a little too crowded and the binding energy slowly declines a little bit.

But there is one, major outlier in this pattern.

Helium-4.

For it’s size, the Helium-4 nucleus is extremely tight. Alarmingly tight. It has well over double the binding energy of Helium-3, and is 20% tighter than those slightly heavier, Lithium nuclei.

You’re not gonna break up Helium-4. Even if it’s trapped inside a larger nucleus.

Radioactive Decay
To understand how special the Helium-4 nucleus is, it helps to go to the other end of the nuclear spectrum.

Really big nuclei, some of the biggest naturally occurring, like Uranium and Thorium, are kind of a mess. They look a lot like blobs, but in a sense a bit disorganized. A little too big for their own good. They’re still bound together, but if it you hit them with a neutron, say, they’d shatter. Sometimes, on rare occasion, they break apart on their own. Spontaneously. This is called radioactive decay.

There are all kinds of ways nuclei can decay. There is plenty of room for nuance, but an easy way to think about it is to ask what kind of particles come out?

This is essentially the way radioactivity was discovered.

Typically, the nucleus just fires out a single particle. For historical reasons those kinds of particles were called: alphas, betas or gammas. Accordingly, we call those kinds of radioactive decay alpha-decay, beta-decay and gamma-decay.

Beta rays turned out to be electrons, and Gamma rays are just photons. But what is Alpha?

Alpha Decay

Here’s a way to think about the alpha decay of a big, honking nucleus. Sometimes clusters of protons and neutrons within that nucleus are bound just a little MORE tightly. That cluster might bounce around the inside of the nucleus, bouncing back against the surface from time to time. Until…A some point… accidentally… it finds itself just a little too far away from the edge of the nucleus.

It’s a random occurrence, but, at that point, it breaks from that residual, nuclear stickiness, and the electrical repulsion of all the OTHER protons in the nucleus...