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Lesson 12: Stability, fusion and fission

Introduction

In this lesson we’ll see how radioactivity causes the nucleus of an atom to become more stable.

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We’ll see how the idea of stability can be used to explain why fission and fusion release energy.  We’ll also see how the nuclei of most of the atoms we find on earth were synthesised in giant stars that exploded.

What do we mean by stability?

Let’s start with what we mean by stability.

A tall wooden block is more stable on its side than resting upright on its end.  If you topple the upright block onto its side then it has no tendency to finish upright again.

How can we account for this?

Stable systems have lower energy

The centre of gravity of the block ended up lower when it toppled over.  In other words the gravitational potential energy of the system decreased.

Where did this energy go?  Initially it turned into the kinetic energy of the moving block.  But when it hit the table this energy was spread out between the particles making up the block, the table and the air.

We have to lift the centre of gravity a little to get the block to topple.  The block only ‘finds out about’ this lower-energy stable state because of the extra energy we put in pushing it over.

Making a system more stable always releases energy

This is the general picture of stability.  Systems become more stable when there is enough energy around for them to ‘discover’ lower energy states.  We have to put some energy in to start the process.  But we get back more energy than we put in.  The difference is called the ‘net energy’.

You can push the block upright again but you always have to put extra energy into the system.  So you can put a system back into a less stable state but it always costs you energy to do it.

When a radioactive nucleus decays it becomes more stable.  The liberated energy is transferred to the particles given off.

Alpha, beta and gamma emission with blocks

Let’s think about a slightly more complex system of two blocks to explain more: a tall, thin block on top of a fatter block.  This tower of blocks is quite unstable.  We can make it more stable in several ways.

Alpha decay is like removing the top block.  Part of the nucleus shoots off leaving something more stable.

Beta decay is like making the top block shorter and fatter.  A neutron changes into a proton.  The resulting nucleus is more stable.

Gamma emission is like turning the top block on its side.  You keep the same blocks but arrange them in a more stable way.

You can also visualize stability in terms of hills and valleys

When you drop to a lower valley, energy is always released regardless of how high you had to climb to get into it.

What determines whether a nucleus is stable?

So what determines the stability of a nucleus?  The answer is very complex and we will only skim the surface here.

If we have two protons fairly close together then they repel each other.  This is because they are both positively charged.  The closer you bring them together the bigger the force of repulsion.

But when they are so close together that they're almost touching they suddenly feel a huge force of attraction.  This is called the strong nuclear force.  The strong nuclear force drops off to zero in a very short distance.

Neutrons also experience the strong force.  They attract both each other and also protons.

Neutrons help to hold the nucleus together

So neutrons provide extra ‘glue’ to hold the nucleus together without the problem of their repelling each other.

With fewer than about 40 protons in the nucleus, you need about equal numbers of protons and neutrons to be stable.  So it is the strong force that holds the nucleus together.  But why are some arrangements stable and some not?

Two's company but three's a crowd

If two protons attract each other then an extra one isn’t treated equally by the first two.  Protons tend to pair off.  Neutrons also tend to pair off.  If two neutrons are attracting each other then they are less helpful at binding protons together.

This pairing means that the majority of stable nuclei have an even number of protons and neutrons.  There are only 4 stable isotopes in existence that have odd numbers of both protons and neutrons.

In big nuclei neutrons increase the distance between protons

Another issue is the very short range of the strong force.  Think of two protons on opposite sides of a large nucleus.  There is a big repulsive force between them because of their positive charge.

But the range of the strong force is so short that the two protons don’t really attract each other.

So bigger nuclei need relatively more neutrons to be stable because it makes the average distance between protons bigger.

Neutrons undergo beta decay if there aren't enough protons around

You may well ask why neutrons don’t simply clump together and ignore the protons?

The answer is that neutrons are very unstable when they are not bound up with protons.  An isolated neutron has a half-life of about 15 minutes.  It decays into a proton, an electron and an anti-electron-neutrino.  This is beta decay.  The electron is the beta particle.

Beta decay happens when there aren’t quite enough protons to completely stabilise the neutrons.

Protons are the most stable particles

An isolated proton is the most stable particle that there is.  Some theories suggest that isolated protons have a half-life of about a trillion-trillion times the age of the universe.

So protons need neutrons to help balance their electrostatic repulsion.  And neutrons need protons to stop them decaying.

240 nucleons is about the maximum size for a nucleus

Imagine producing nuclei by joining together random numbers of protons and neutrons.

Any nucleus with more than about 240 nucleons in any combination won’t stay together for long.  This is like what happens to a really tall tower built from toy wooden blocks.  Even though the tower is temporarily stable, even a tiny push will knock it over into a lower energy (and hence more stable) state.

Fission means breaking apart a nucleus

Breaking apart a large nucleus into smaller pieces is called ‘fission’.  Just like knocking over our tower it liberates energy.

Alpha decay is a special case of fission where one piece is very big and the other is very small.  Big nuclei emit alpha particles because it makes them smaller (i.e. fewer nucleons) and so more stable.

But what about the random nuclei we’ve made that aren’t too big?

Too many neutrons or protons means unstable

About half our randomly produced nuclei would have far too many protons compared with neutrons and would simply fly apart.

The other half would have too many neutrons compared with protons.  Neutrons will decay to form protons until the ratio is stable.

Stable or nearly stable

A very small proportion of nuclei we’ve randomly created will have exactly the right numbers of protons and neutrons to be stable.  And a similar sort of number will have ALMOST the right numbers to be stable but will decay if there’s enough internal energy available.

So we happened to create some nuclei that were nearly stable.  Are these the radioactive nuclides we find on Earth?

Almost everything created unstable will have changed by now

Now let’s imagine that we fabricated millions of different combinations of nuclei just once about 5 billion years ago.  After fabricating our millions of random nuclides we imagine stopping and never adding any more protons or neutrons.

Which nuclei would we expect to see now, 5 billion years later?

We’ve already seen that really big nuclei and nuclei with too many protons or neutrons won’t stay in the same form.

Obviously we will see the tiny proportion of nuclei that happen to have been created stable.

But what about the ones that were created NEARLY stable, like radon-220, which we’ve been reading about?  Surely those are the radioactive isotopes we find on Earth?

Well you would hardly see any of those either because the vast majority will have decayed into something stable by now.

All you see is the products of the long natural decay chains

The only radioactive nuclides that we'll see are those being produced all the time by the decay of ‘parents’ with a very long half-life.

These are called decay chains.  There are three major ones, headed by uranium-238, uranium-235 and thorium-232.

Uranium-238 has a half-life of about 5 billion years so about half of what we originally made will have decayed into other nuclei.  Uranium-235 has a half-life of about 700 million years so only about 1% of the original nuclei won’t have decayed into other nuclei.  And thorium-232 has a half-life of about 14 billion years so most of those nuclei remain undecayed.

The decay chains are defined by nucleon number

Let’s look at the uranium-238 decay chain as an example.

As a uranium-238 nucleus decays by alpha emission it gets smaller and smaller – and so more and more stable.  Eventually it arrives at lead-206 which is completely stable.

Each alpha particle takes away two protons and two neutrons.  But there were fewer protons to begin with.  So losing the two protons has a bigger effect.  Neutrons need protons to be stable.

Beta decay will change enough neutrons into protons for the neutrons to be stable again.  Two is normally enough.  Beta decay doesn’t change the nucleon number.

Alpha decay causes the uranium-238 nucleus to get smaller 4 nucleons at a time.  It's only alpha decay that can change the nucleon number and then only by 4 nucleons, not 1 or 5 or any other number.

In other words, each nucleon number only belongs in one particular decay chain.  The decay chain is defined by the nucleon numbers.

Because beta decay changes the number of protons each element appears several times.

The missing 4th decay chain

There are some nucleon numbers where we don't find any nuclei on Earth: 237, 233, 229, 225...down to 209.

It looks like there is a whole decay chain that has disappeared!  And indeed there is.

The decay chain headed by neptunium-237 (with a half-life of a mere 2 million years) has completely decayed.  Only the last link remains of bismuth-209 decaying very slowly to thallium-205.

So almost all of the naturally occurring radioactive nuclides come from one of these three existing decay chains.  They are constantly produced as the nuclei of the very long-lived parents decay down the chains normally heading for stable lead.

Nuclei are made in the centre of stars

Now we started off this exercise by imagining this one-off period of synthesis that happened 5 billion years ago.  We imagined having enough protons and neutrons available to make any combinations we could think of.  And we said we would see anything that happened to be completely stable or any decay product from a very long-lived parent.

So where was this factory for making vast numbers of random nuclei?

Fusion means joining small nuclei together

The first part of the story takes place at the centre of all stars.  Stars are made of hydrogen nuclei, in other words protons.

The protons move fast enough and are close enough together for some of them to join up and form larger nuclei.  Joining together protons to form a bigger nucleus is called ‘fusion’.  The process is actually very complex and rare but stars are very big so overall it happens a lot.

Stars much bigger than our Sun have much higher temperatures and pressures at their centres.  They can fuse both protons and smaller nuclei to make bigger ones.  The biggest stable nucleus that can be formed is iron-56.

A supernova spreads the nuclei formed out into space

Big stars like this end their lives in a huge explosion called a supernova.  A supernova produces vast numbers of neutrons.  Neutrons are uncharged so they can get very close to a positive nucleus.  The neutrons are absorbed and form even bigger nuclei.  Beta decay changes neutrons into protons.

The early universe contained only hydrogen, helium and a little lithium.  All the other elements are made in stars.  Supernova explosions spread the oxygen, nitrogen, chlorine, iron and all the other elements throughout the universe.

During the explosions themselves all the gold, lead, uranium and other heavy elements were made.

As soon as they were made the unstable nuclides started to decay into more stable ones.

The Earth is made from supernova nuclei (and so are we!)

Our Sun is one of the countless stars formed from a cloud of hydrogen laced with heavier elements from at least one supernova.  The hydrogen formed the sun and the trillions of tonnes of dust made of  heavier elements formed the planets, the Earth, all life and us!

So we’ve seen how stars can randomly shuffle protons and neutrons to produce the radioactive nuclei we see on Earth today.  Potassium-40 is the most abundant radionuclide in the Earth's crust.

Almost all the others are in these long decay chains.

Making short decay chains naturally and in reactors

Potassium-40 has a one-step decay chain and a billion-year half-life.  Isotopes with a shorter half-life can also be synthesised naturally.

For example carbon-14 is continuously created in the atmosphere because of cosmic rays.  This decays in a one-link chain to nitrogen-14.

In lesson 15 we'll see how carbon-14 decay can be used to find the age of things that were once alive.

The other place where ‘artificial’ decay chains are created is in nuclear reactors.  Neutrons are used to make large nuclei like uranium-235 fission into two new smaller nuclei.

Nuclei made from splitting big nuclei are always unstable

Big nuclei need lots of neutrons to be stable.  Smaller nuclei need fewer neutrons to be stable.

But when a big nucleus splits each daughter has about the same proportion of protons and neutrons as the (larger) parent.  This is too many neutrons for a smaller nucleus and so beta decay causes neutrons to change into protons.

So each new nucleus caused by fissioning a large nucleus sits at the top of its own decay chain.  These short, artificial decay chains happen much earlier in the periodic table than the long natural ones.

Transuranic elements: big, unstable, artificial nuclei

When some big nuclides like uranium-235 absorb a neutron it makes the nucleus so unstable it fissions almost immediately.  Other nuclides, like uranium-238, can absorb neutrons and just get bigger.  (Remember beta decay can change neutrons into protons).

These very large artificial nuclides, like plutonium, are called ‘transuranic’ because they are ‘beyond uranium’ in the periodic table.  All transuranic nuclei decay by alpha emission to make their nuclei smaller.  Beta emissions keep the ratio of protons to neutrons stable.

Sometimes transuranic elements can feed into the natural decay chains.  For example plutonium-239 decays into uranium-235 with a half-life of about 25 000 years.

The amount of uranium-235 formed by plutonium-239 decay is minuscule compared with the trillions of tonnes occurring naturally in rocks.

Fuse up to iron.  Fission down to iron.

Both fission and fusion release energy by making the nucleus more stable.

You always have to go uphill, in other words put energy in, to get either process to happen.  For example we’ve seen that to fuse two protons you have to do lots of work overcoming the electrostatic repulsion.

Once you get to iron-56 there is no benefit to either fission or fusion because they both involve going ‘up hill’.  This means you have to put in more energy than you get out and you end up with something less stable!

So we’ve seen how the idea of stability explains the existence of the natural decay chains.  We’ve also see how fission and fusion cause energy to be released when protons and neutrons are arranged in more stable ways.

Back to Summary of Radioactivity and Atomic Physics Explained