Nuclei

Radioactivity is super-cool but it leaves you with an unquenched curiosity. It is one of the concepts in Physics where your brain jumps from one question to another without finding the answer to either of them (mostly). Or maybe we are just really dumb. Before we dive into an array of explanations and theories, it is important to note that as of now, when we haven’t even seen an atom in its entirety or even a molecule, being able to explain how one type of element changes into another, or becomes unstable mostly works on theories, mathematics and experimental data. 

A Nucleus Is Not Just Protons and Neutrons : The Standard Model – A Brief Intro

If we think of a nucleus as a tiny cluster of protons and neutrons, we cannot explain its complicated traits like its extent of stability, whether or not it will decay, why the ratio of neutrons and protons changes as we move from lighter to heavier elements, and such.

Protons and Neutrons have a lot of quantum stuff going on that is so random that you need mathematical models to predict the results. Instead of making models for everything random, Physicists started smashing particles as a probe into the target particle they wanted to study. Every interaction between different kinds of particles yielded a plethora of results. Even the same types of interactions looked different on observing them differently.

That being said, when a proton or a neutron is probed under normal conditions, it shows a swarm of three different kinds of particles inside. For simplicity, they are named as quarks. (Reference)

The Quark Structure

In quantum physics, the way you explain various things depends on how zoomed in you are to them. The nucleus, at a still smaller scale, seems to be made up of cluster of clusters of quarks. Quarks are indivisible entities (maybe?) whose behaviours are explained by a branch called Quantum Chromodynamics. Experimentally, neutrons and protons are observed to be further made up of these quarks. 

Neutrons and Protons have three quarks each containing two flavours (types) : up and down quarks.

Keeping the nucleus intact works at two levels, first the quarks in the nucleons must co-exist, and then the nucleons themselves must survive in their original form. Now, quarks are held by what we call the Strong Force. This is carried by exchanging their very own force-carrying particles called Gluons. Here’s how it works.

Technically, the quarks are inseparable due to such strong force between them which acts like an elastic band.

The second level is when these quarks have formed groups of three and gathered as individual neutrons and protons. They are able to do so due to a property called Colour. It is intrinsic like the spin of an electron and of course, it is not literally a colour but three specific names of colours (Red, Blue and Green) given to something you will never understand (neither do we). In a swarm of up and down quarks, when those with these three colours scoop up as two up and one down or one up and two down, they make up the protons and neutrons respectively. 

This 2-level stability is not like the one we study in high school textbooks, where the strong force cutely binds the nucleons. It is rather a much indirect process. It actually exists between the quarks making them quite inseparable through something called Colour Confinement. The interaction between quarks is due to their colour and when the three colours come together, they tend to neutralize this property the way a negative charge neutralizes a positive.

When this happens, there is no reason for the strong force to extend between protons and neutrons because they are colour-neutral except that the quarks create another type of exchange particles called Pions. 

Pions have their own colour and they sneak out of the protons and neutrons to establish a bond between them, as carriers of the ‘Residual’ Strong Force.

Tl;dr quark-quark pairs are bonded by gluons, nucleon-nucleon pairs are bonded by pions.

Why do we need Neutrons?

The only thing that makes neutrons different from protons is the variation of a single quark. But the protons can still exchange the residual strong force among themselves. There are two forces in action inside a nucleus, and their nature becomes prominent at this point. The electromagnetic repulsion does not limit the protons to act on their neighbours only, while the strong force does. Pions carrying the force between nucleons are virtual particles, meaning they only exist for an absurdly short stretch of time. This limits the range of nucleons it can reach to only the adjacent ones, making the residual strong force short-ranged. 

Each proton can repel every other proton regardless of the separation. It would not matter if they have the strong force, too much repulsion will eventually take over and rip the nucleus apart. That’s the reason Neutrons club in a nucleus and provide extra strong force minding their own business, being electromagnetically neutral.

In smaller nuclei, an equal number of neutrons as protons is enough to overcome the repulsion. As we move up to higher elements, they start having bigger nuclei due to larger atomic numbers. Of course more protons will require more neutrons, but neutrons start to double. Why this sudden increase in proportion? 

A nucleus cannot be compressed because the strong force between quarks has a minimum distance below which it starts getting repulsive. So, that means, the nuclear density must remain almost the same.  

Increasing protons will increase the repulsion manifold as that will not depend on the adjacent nucleons only. This means that they will be pulled apart from distant protons even if they are bound with the ones in close proximity. And so, neutrons start to outnumber the protons so that even if repulsion takes over and proton loses its bond, a neutron can catch it before it tries to fly out of the nucleus. This explains why we observe more neutrons in heavier elements. You can visualize with the following animation how when one of the bonds (lines) disconnects, it quickly joins somewhere else. The dots can be seen as various nucleons. 

Excess is not good

Too many protons are clearly problematic but a lot of neutrons can cause instability as well. We have observed isotopes of smaller elements with more neutrons than protons decaying radioactively, and it has been clear that more neutrons are not always the solution. 

Wherever there’s a force, there’s energy being utilised. The energy keeping a nucleus together is called Binding Energy and it is shared between all the nucleons. In nuclear labs, when Physicists decide to carry out a fission reaction, they calculate the energy to put in by seeing how much energy is binding a single nucleon. Higher the binding energy per nucleon, more stable is the nucleus. But this is one way of looking at the concept of stability. 

Apart from that, theoretically, Physicists know that nucleons tend to pair up like electrons do and are arranged in a nucleus following the Pauli Exclusion Principle. Based on this, a semi-empirical formula with partial experimental proofs has been made to calculate the binding energy based on the number of nucleons an element contains. (Reference)

Also look up: Nuclear Shell Model.

Semi-Empirical Mass Formula

This formula contains a pairing term, which takes into account the expected pairing of the nucleons. It is derived empirically and has stood precise with several actual observations. The semi-empirical formula concludes that for most nuclei, even-even numbers of nucleons are usually most stable, while even-odd lesser and odd-odd the least.

It has also listed Magic Numbers of nucleons for an ideal stable nucleus. Some of the elements having such numbers are helium, oxygen, calcium, nickel, tin, lead.

But we are not done yet. Stability cannot be explained with a single theory. It involves considering a lot of traits of a nucleus which we cannot even experimentally observe. At some places, nuclei prefer binding stability while at others pairing messes things up. 

An example being Tritium (which has only one proton so no electromagnetic repulsion, and two neutrons), which is so cool to think about. It does not exist naturally but when made in labs, it has a half-life of twelve years (indicating a rather stable radioactive nucleus)!

Radioactive Decay

When an element starts having existential crisis, the only cool thing left in its life is Radioactivity (except for Radium, it glows, or does it?). There are mainly two types of decays a nucleus can choose from to achieve stability: Beta Decay and Alpha Decay.

Both of them use different ways to unfold. Beta decay uses the Weak Force of interaction, while Alpha decay is due to a quantum phenomenon called Tunneling.

Beta Decay

The weak force which facilitates the beta decay process changes the flavour of quarks, like converting an up quark to down (proton to neutron) or vice-versa. Its carrier particle is a W Boson responsible for the transformation. (See: Beta Decay)

Alpha Decay

Alpha decay is peculiar in the sense that it works on probabilities. An alpha particle (Helium nucleus) is emitted. Particles as waves can have an area of probability each part of which has varying chances of finding that particle. Emitting an alpha particle is difficult for a nucleus considering the strong force it is bound with. This creates an energy barrier and usually it is almost negligibly probable for the particle to cross it. But quantum tunneling still permits it. 

The nuclei which are able to jump this barrier and show alpha decays simply have a better probability. Why this happens? We cannot figure it out without getting into much complicated quantum mechanics (go ahead, if you love Sprite).  But how do elements decide their type of decay? (We have not the faintest of ideas.) (See: Alpha Decay)

Other types of decays: Gamma Decay, Electron Capture.

Do Radioactive Elements Glow?

Sorry to tell you that the green light seen in sci-fi movies you thought to be coming out of radium is not actually the case.

Radioactivity releases ionising radiation which is powerful enough to excite the atoms nearby to higher states making them emit visible radiation (glow) as they come down. This phenomenon is known as Radioluminiscence.

Another indirect yet bizarre phenomenon is the Cherenkov Radiation. This is emitted as visible light when high-speed electrons (from a radioactive decay, for example) are slowed down while passing through a dielectric medium like water.

The radioactive elements are not actually glowing. For them to glow, they must emit radiation in the visible spectrum. But the only electromagnetic radiation we observe as a direct result of radioactive decays are Gamma Rays.

And here’s about the most inspiring Physicist in the hearts of many: The Great Marie Curie