# Electric Charge Conservation for Nuclear & Elementary Particle Reactions

Instructor: Matthew Bergstresser

Matthew has a Master of Arts degree in Physics Education

The conservation of electric charge is a fundamental law of the universe. In this lesson, we will discuss how electric charge is conserved when the atom undergoes radioactive decay, and elementary particle annihilation.

Isaac Newton, who is considered the grandfather of physics, was also an alchemist. Alchemy was the pursuit of changing metals like lead or iron into gold. Although Newton never succeeded in producing this transformation, alchemy laid the foundation for modern chemistry.

We now know that elements can transmute, or change from one element to another, but it is not through a chemical process. It is a nuclear process that happens in the nucleus of the atom. Let's see how it works.

## The Nucleus

The nucleus of the atom contains two elementary particles: the proton and the neutron.

• Protons are positively charged, and have a mass of 1 AMU (atomic mass unit, roughly equal to 1.66 x 10-27 kg).
• Neutrons have slightly more mass than a proton, but their masses can be estimated to be 1 AMU each. A neutron, though, has no electric charge. You can remember this by thinking the neut in neutron represents 'neutral'.

For a nucleus to be stable, the ratio of neutrons to protons has to be within a certain range. Elements with atomic numbers less than 20 are stable with a 1 neutron to 1 proton ratio. Atomic numbers ranging from 21 through 83 are stable when they have 1.5 neutrons for every proton. If an isotope's (specific version of an element) neutron to proton ratio is not within these ranges, it will undergo radioactive decay.

Radioactive decay is the spontaneous reconfiguration of an isotope's nucleus to stabilize its neutron to proton ratio. Let's go through how neutrons and protons can turn into each other.

## Nuclear Particle Switch

First, let's look at the notation used to represent nuclear reactions:

### Proton Decay

Let's say that a specific isotope has too many protons compared to the number of neutrons in its nucleus. Therefore, that proton will turn into a neutron.

The bottom numbers represent the electric charge of the particles. The proton on the left has a charge of 1. On the right side of the yields sign (arrow), a neutron (n) is listed along with two other particles. The 0/1 e is called a beta-plus particle or a positron. It is the positive version of an electron, which is anti-matter.

Notice that the bottom numbers add up to equal the charge on the proton. The particle on the far right is a neutrino. It has no charge and no almost no mass, but it's required in the equation for the conservation of energy and momentum.

### Neutron Decay

If a nuclide has too many neutrons, a neutron will turn into a proton.

Notice that a neutrino shows up along with a standard electron, also called a beta-minus particle. The total charge is conserved because the addition of the electric charge values for the particles on the right equals the electric charge of the particle on the left.

## Nuclear Decay

Now, let's look at the decay of the nucleus of an unstable atom. Electric charge is always conserved in these processes. We will go through both types of beta-decay, but leave out the neutrinos since they are neutral.

### Beta-plus

Carbon-10 has the proton-neutron ratio of 4 neutrons to 6 protons. It needs more neutrons to be stable, therefore a proton can turn into a neutron via beta-plus decay.

Notice that the electric charge is conserved. The carbon-10 has a +6 charge, and the +5 charge of boron added to the +1 charge of the positron equals +6.

### Beta-minus

Carbon-14 has the proton-neutron ratio 8 neutrons to 6 protons, and this is not in the stable range we previously discussed. A neutron has to turn into a proton, and it does this via beta-minus decay.

Again, the net electric charge on both sides of the yields sign is identical. +6 on the left, and (7 +(-1)) = +6 on the right.

## Particle Annihilation

One of the Holy Grails for physics is harnessing the power of matter-antimatter collisions. The famous book by Dan Brown, ''Angels and Demons'' is centered around this phenomenon.

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