# Conservation of Nucleon Number: Definition & Examples

Instructor: Matthew Bergstresser
There are several conservation laws in science. This lesson will focus on the conservation of electrical charge and mass dealing specifically with the nucleus of the atom.

## Inside the Atom

The atom consists of two main parts: the nucleus, and the area surrounding the nucleus called the electron cloud. The majority of the mass of the atom is the nucleus because it houses protons and neutrons. Each of these particles has a mass of roughly 1.67 x 10-27 kg. You may wonder how this extremely small mass can even be considered to be larger than an electron. It is. An electron's mass is 9.109 x 10-31 kg, which is over 1700 times smaller than a proton or neutron! Since these subatomic particles' masses are so small we normally define the mass of a proton and neutron as 1 atomic mass unit, or AMU, which is the approximate average of the proton rest mass and neutron rest mass.

The coulomb is the unit of electrical charge, and electrons have a charge of -1.6 x 10-19 C. Protons have the same electrical charge, but positive. Again, such a small number is cumbersome to work with so we define the charge of an electron as approximately -1. Protons, therefore, have a charge of +1. Neutrons have no electrical charge.

A nuclide is a specific version of an element defined by how its nucleus is constituted. The format for representing the mass and electrical charge in a nuclide is shown in Figure 1. X represents the symbol of the element, N represents the mass of the nuclide (protons + neutrons), and Z represents the nuclear charge (number of protons).

### Conservation of Mass and Electrical Charge.

Now that we know the basics parts of the atom, and how to represent any nuclide's mass and electrical charge, we will shift our focus to two conservation laws: the conservation of mass, and the conservation of electrical charge. Mass and electrical charge can not be created, nor can they be destroyed; their whereabouts must always be accounted for. Think of it as an atomic version of monetary book keeping. Instead of keeping track of where money goes, we are tracking the mass and charge of a nuclide as it changes.

When a nucleus's neutron to proton ratio is not in the range of 1:1 to 1.5:1 it is unstable or radioactive. A radioactive nucleus spontaneously decays, giving off a variety of particles. Although other types of emissions were eventually discovered, there are three basic particles and one type of electromagnetic radiation that are typically emitted from the nucleus. The only emitted particle having significant mass is called an alpha-particle (α). It has a mass of 4 AMU and a +2 electrical charge, and is basically the same as the nucleus of a helium atom. There are two massless charges that can be ejected by the nucleus. One is a beta-minus particle (Β-) which has a -1 charge, and the other is a beta-plus particle (Β+) which has a +1 charge. A gamma ray (γ) is pure electromagnetic radiation energy which has no mass nor any electrical charge.

Let's go through some examples of how mass and charge can be tracked when a nucleus changes due to its decaying using a nuclear equation.

#### Alpha Decay

Uranium-238 decays into thorium-234. The numbers after the element's symbol are the mass numbers, and notice that 238 and 234 are not equal. 4 AMU are missing. We can account for this mass because U-238 undergoes alpha decay, and a nuclear equation shows how the mass and electrical charge is conserved.

The mass numbers located in the top spaces show a conservation of mass, and the nuclear charge numbers located in the bottom spaces show a conservation of electrical charge.

#### Beta-minus Decay

Lead-210 is radioactive and decays into bismuth-210 via beta-minus decay. The mass in this transmutation (the change of one element into another) is the same, but different elements have different nuclear charges, so we have to account for this discrepancy in electrical charge.

Notice that the mass on the left side of the equation equals the total mass of both parts of the right side of the equation. The charges are also conserved.

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