Nuclear Reactions

Through the previous articles we have pieced together the purpose of each component of the atom (protons, neutrons, and electrons) and we saw what happens when we move these particles around. Electrons are exchanged between atoms causing new bonds to form during chemical reactions. Nuclear reactions occur when there isn't a proper balance of neutrons and protons in the nucleus. We saw that in some cases, neutrons and protons will transform into each other if doing so would put the nucleus in a much lower energy state.

So what exactly does it mean to be "in a lower energy state"? When something moves from a high energy state to a lower energy state, it gives off energy. On the other hand, if you want to move something from a low energy state into a higher energy state, you have to put energy into it. The lower an energy state something is in, the more energy it will take to get it back up to a higher energy state.

Changes in Energy State

Changes in Energy State

For example think of a big rock sitting halfway up a hill. It will take a lot of energy to roll the rock from the halfway point to the top of the hill, but it will take much more energy if we start all the way at the bottom. Note also the the rock will naturally want to roll to the bottom if you give it a push. In this case the top of the hill is the highest available energy state and the bottom of the hill the lowest with respect to the Earth's gravitational field.

Don't try this at home

Don't try this at home

For the protons and neutrons in a nucleus the tighter they are bonded, the lower the energy state of that system and the more energy it would require to take them apart. Now obviously it takes more energy to disassemble larger nucleii than smaller ones simply because there are more nucleons. A big wall made of many bricks will take more energy to disassemble than a smaller wall made of fewer bricks, but that doesn't mean that the bricks in the larger wall are more strongly stuck together than those in the smaller wall. A better comparison would be the total energy to take apart the wall divided by the total number of bricks if we really want to know how strongly the bricks are stuck together.

Unless of course you have dynamite in which case it doesn't really matter how many bricks there are

Unless of course you have dynamite in which case it doesn't really matter how many bricks there are

In order to compare how tightly bonded two nucleii are, we use the total energy needed to disassemble it divided by the total number of protons and neutrons. This gives us the average binding energy per nucleon and we can use it to better compare how tightly bound different nucleii are. The lower the energy state of a nucleus, the more energy it takes to pull it apart and the higher its binding energy per nucleon will be. If this sounds counter-intuitive, think back to the rock. The lower the energy state of the rock, the more energy you need to use to get it up the hill.

    Binding Energy per Nucleon of Various Isotopes

 

Binding Energy per Nucleon of Various Isotopes

The graph above shows the average binding energy per nucleon of various isotopes. The lightest ones are on the far left and include hydrogen (H), helium (He), lithium (Li), etc. These are the elements at the top of the periodic table. On the right side are the heaviest ones such as uranium (U) which are near the bottom of the periodic table. The atom with the highest binding energy per nucleon is nickel, specifically nickel-62 (Ni-62), closely followed by iron-56 (Fe-56). These two isotopes have the most tightly bound nucleii of all and, as you may have guessed, sit near the middle of the periodic table. Note that nickel is element number 28 and iron is element number 26 if you're trying to find them on the periodic table. The number "62" in Ni-62 and "56" in Fe-56 is the total number of nucleons (protons plus neutrons).

Image courtesy of Wikimedia Commons   The Periodic Table of the Elements

Image courtesy of Wikimedia Commons

The Periodic Table of the Elements

Ok so we've established that nucleii will try to put themselves in lower energy states which means creating tighter bonds between their protons and neutrons. We also know that it isn't the lightest elements (like hydrogen) nor the heaviest elements (like uranium) that are the most tightly bound. The ones in the middle (like iron and nickel) have the most tightly bound nucleii and are therefore at the lowest energy state of all the isotopes. In general, nuclear reactions involving heavy isotopes will result in them becoming lighter and reactions involving lighter isotopes will result in them becoming heavier. Both want to end up somewhere in the middle near iron-56 and nickel-62 because this is the lowest energy state. The question then becomes, are all the isotopes slowly turning into iron and nickel?

To answer this let's go back to the rock on the hill. If you let a rock go it will roll downhill, no surprises there. However anyone who's ever tried this in practice knows that the rock rarely makes it all the way to the bottom without being snagged and stopped by something. There are small local low energy states on the way down that the rock can get caught in and stay indefinitely.

Rock becomes trapped in a small hole and isn't able to escape without a push

Rock becomes trapped in a small hole and isn't able to escape without a push

Things cannot move from low energy to high energy unless you add energy to them so once the rock gets caught in a local low energy state, it will stay there forever until someone or something gives it enough of a push to escape and continue rolling down the hill. The same is true of nuclear reactions, a nucleus will try to re-arrange itself to move towards the lowest energy state but if it happens to put itself into a stable state along the way, it will stay there. We can see this on the chart of the nuclides, all the black squares are stable nucleii. The coloured ones are unstable (radioactive) and will slowly change until they eventually become one of the stable (black) nucleii. Some will eventually become iron or nickel if they are already close but the ones that are further away will likely become some other stable isotope.

Image courtesy of Brookhaven National Laboratory   Of all the possible combinations of neutrons and protons, only a few are stable

Image courtesy of Brookhaven National Laboratory

Of all the possible combinations of neutrons and protons, only a few are stable

We know that nucleii can convert neutrons into protons and vice-versa to move towards stability but there are some more spectacular reactions available as well. Some really heavy nucleii will actually split themselves to become two smaller nucleii, releasing a lot of energy. This is called nuclear fission and is how nuclear reactors are able to produce power. On the other hand, really light nucleii if they are under enough pressure or given enough energy can actually stick or fuse together into heavier nucleii, also releasing a lot of energy. This is called nuclear fusion and is how stars produce their energy. They both result in a release of energy because the nucleii end up moving into a lower energy state after the reaction.

    Nuclear reactions result in more tightly bound nucleii

 

Nuclear reactions result in more tightly bound nucleii

So there you have it, nuclear reactions are the result of nucleii trying to move towards a more tightly bound nucleus (lower energy state). This causes nucleii much larger than iron and nickel to typically become smaller and nucleii smaller than iron and nickel to typically become larger. Although they are trying to get to the lowest possible energy state, unstable (radioactive) nucleii will typically end up becoming one of the many stable nucleii along the way and stay there.