KAHIBARO
Table of Contents
Counting Nucleons
Mass number tells us how many particles are in the nucleus of an atom. The nucleus contains protons and neutrons, which are together called nucleons. If a nucleus has $Z$ protons and $N$ neutrons, then its mass number $A$ is
$$
A = Z + N
$$
This is a whole number, because it is simply a count of particles.
The mass number $A$ is the total number of protons and neutrons in the nucleus.
$$
A = Z + N
$$
It is not the same as atomic number, and it is not the same as atomic mass.
What Mass Number Means
Mass number identifies how many nucleons are packed into a particular nucleus. Since protons and neutrons make up almost all of the atom's mass, the mass number is closely related to the size of the nucleus in terms of particle count. However, mass number is not measured in kilograms or atomic mass units. It is only a number.
For example, a carbon nucleus with 6 protons and 6 neutrons has
$$
A = 6 + 6 = 12
$$
so its mass number is 12.
A carbon nucleus with 6 protons and 8 neutrons has
$$
A = 6 + 8 = 14
$$
so its mass number is 14.
These are both carbon because they have the same number of protons, but they have different mass numbers because they contain different numbers of neutrons.
Symbol Notation
A nucleus is often written in the form
$$
{}^{A}_{Z}X
$$
where $X$ is the chemical symbol, $Z$ is the atomic number, and $A$ is the mass number.
For example,
$$
{}^{12}_{6}\mathrm{C}
$$
means carbon with mass number 12.
Similarly,
$$
{}^{14}_{6}\mathrm{C}
$$
means carbon with mass number 14.
From this notation, the number of neutrons can be found by rearranging the formula:
$$
N = A - Z
$$
If you know mass number $A$ and atomic number $Z$, then the neutron number is
$$
N = A - Z
$$
Examples
The table below shows how mass number is determined for several nuclei.
| Nucleus | Protons $Z$ | Neutrons $N$ | Mass number $A$ |
|---|---|---|---|
| ${}^{1}_{1}\mathrm{H}$ | 1 | 0 | 1 |
| ${}^{4}_{2}\mathrm{He}$ | 2 | 2 | 4 |
| ${}^{12}_{6}\mathrm{C}$ | 6 | 6 | 12 |
| ${}^{16}_{8}\mathrm{O}$ | 8 | 8 | 16 |
| ${}^{235}_{92}\mathrm{U}$ | 92 | 143 | 235 |
As an example, for uranium-235,
$$
N = A - Z = 235 - 92 = 143
$$
So this nucleus contains 92 protons and 143 neutrons.
Mass Number Versus Atomic Mass
The words sound similar, so beginners often confuse them. Mass number is a count of nucleons. Atomic mass is the actual mass of an atom, usually measured in atomic mass units, and it is not generally an integer exactly equal to $A$.
This difference happens because protons and neutrons do not each have exactly mass 1 in atomic mass units, and also because nuclear binding affects the total mass.
Do not confuse these ideas.
Mass number, $A$, is a whole-number count of protons and neutrons.
Atomic mass is a measured physical mass and is usually not exactly equal to $A$.
Why Mass Number Is Useful
Mass number helps distinguish nuclei of the same element that have different neutron counts. It is therefore an essential label in nuclear physics. When a nucleus is named, the mass number is often written after the element name, such as carbon-12 or uranium-235.
This number is especially useful because many nuclear properties depend strongly on how many nucleons are present.
Simple Visual Picture
A nucleus can be pictured as a cluster of protons and neutrons. The mass number is just the total count of all particles in that cluster.
In this drawing, if there are 4 protons and 5 neutrons, then
$$
A = 4 + 5 = 9
$$
A Quick Check
If a nucleus has 17 protons and 18 neutrons, then its mass number is
$$
A = 17 + 18 = 35
$$
If a nucleus has mass number 40 and atomic number 20, then its neutron number is
$$
N = 40 - 20 = 20
$$
These simple calculations are the main use of the idea.
Key facts about mass number:
$$
A = Z + N
$$
$$
N = A - Z
$$
Mass number is a count of nucleons, not a measured mass.
Final Idea
Mass number is one of the most basic labels of a nucleus. It tells us how many nucleons the nucleus contains in total. Once you know the number of protons and the mass number, you can immediately find the number of neutrons.