# Nuclear Notes

### The Introduction to Nuclear Physics

The atom consists of a nucleus in the center, of protons and neutrons, surrounded by electrons. The number of protons and electrons are usually the same. The number of protons is the “atomic number” of the periodic table, used to order each element. For example, since a hydrogen atom has one proton, it is put first.

The protons and electrons have opposite charges, leading to them being attracted to each other. The protons have positive charges, and the electrons have negative. The neutron has a neutral charge, attracted to nothing. The model of how the elctrons work is insteresting. The electrons actually sort themselves into layers. The first layer, above the nucleus, holds two electrons. The second holds eight, and the third holds eighteen. The formula here is that, if the variable n means the layer in order from the nucleus, the formula is 2(n2).

2(12) = 2

2(22) = 8

2(32) = 18

A stable atom needs its overall charge to be zero. Saying Z is the atomic number, or the number of protons, there needs to be Z protons and Z electrons. The chemical properties of an element are determined by Z. If N means the total number of neutrons in a nucleus, that means that the formula for atomic mass, A, is A = Z + N (because an electron has very little mass, so technically this is a rough estimate for finding atomic mass).

Difference in the number of neutrons usually does not affect an atom since it has no charge, so an atom with a different number of neutrons but the same number of protons and electrons are called an isotope.

Since this means the properties of an atom are only determined by the number of protons, or sometimes its atomic mass, we can use this notation to write an element in the nuclear field:

AZX

(but the A and Z are not spread and are on the same character)

Since the atomic mass is just usually Z, the atomic number, multiplied by 2, we may just drop the Z and be left with AX. Carbon could be written as 126C or just 12C. If an atom does not have a charge of zero, or an unstable atom, we write it as 12C*. When it has excess energy it is called an isomer.

There are two forces in an atom – a strong force and the electric force. The strong force is simply a force that can let two subatomic particles stick together. Protons are not able to stick together because of the strong force, most likely because they would repel because they are of the same charge. But neutrons have no charge, so the strong force of them together is enough for them to stick and form a nucleus.

We can’t add too many neutrons to the nucleus, even though they do not contribute (or contribute very little) to the repulsion of any part of the nucleus. But a nucleus that is isolated by itself will only last around 15 minutes before falling apart into a proton, electron, and antineutrino.

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n → p + e + ve .

This is actually an example of nuclear decay named beta decay, because the electron here is the same as that is called a β (or beta) particle, a form of energy emitting as a form of radioactivity.

There is actually several elements that do have a few extra neutrons and are still stable. Below is a chart of what the stability can be between neutrons and protons in a nucleus:

The reason the chart only goes to Z=83 is because there is just so much unbalanced energy after that that it becomes too unstable to keep adding protons and neutrons. This means they are radioactive because they start to emit particles of energy.

So this is why nuclear decay occurs. It is because it is an isotope, isomer, or both, and the excess energy will start to make the atom break and start giving off excess energy in a form of radiation.

There are three different particles that are emitted as radiation due to decay:

• α (alpha) particles, which are helium nuclei, with 2 protons and 2 neutrons
• β (beta) particles, which are electrons and antineutrinos (although the antineutrinos may be absorbed in a second beta decay)
• γ (gamma) particles, which are very energetic light rays

We can easily differentiate these three particles by checking how they deflect a magnetic field.

Alpha particles are positively charged, beta particles are negatively charged, and gamma particles are neutrally charged.

Gamma decay happens when an isomer with too much energy decays completely. A gamma particle is thrown off as a result of the energy leaving.

12C* → 12C + γ

Alpha decay happens when a nucleus has too many protons. The protons start to decay off due to the other protons repelling them away. The protons actually pick up two electrons on the way.

23892U → 23490Th + α

Beta decay, like said before, is when an isolated proton splits off into a proton, electron, and antineutrino.

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146C → 147N + e + ve .

Now we get to nuclear fission. Nuclear fission is when neutrons, possibly obtained from other decay, is shot at a large nuclei like Uranium. This breaks it into two possibly unequal parts. When more neutrons are shot from this fission into other nuclei… there is a loop made before there are no more nuclei to shoot. When fission happens, it gives off enormous amounts of energy. In a controlled process, a power source could be made through the heat energy produced by the fission. In an uncontrolled process, it’s an atomic bomb.

Summary

Because of imbalances in energy, nuclear decay happens in different timespans. Alpha decay is when 2 protons and 2 neutrons leave the nucleus because the nucleus has too many protons. Beta decay happens because an isolated neutron hangs around the nuclei because there are too many neutrons to balance the protons. So they break up into a proton, neutron, and antineutrino. Gamma decay occurs because a nucleus is in an excited state,  unable to be stable. So it emits a photon, or gamma particle.