MASS NUMBER: WHAT IT IS AND HOW TO GET IT (WITH EXAMPLES) - PHYSICAL - 2025

The mass number or mass number of an atom is the sum of the number of protons and the number of neutrons in the nucleus. These particles are designated interchangeably with the name of nucleons, therefore the mass number represents the amount of them.

Let N be the number of neutrons present and Z the number of protons, if we call A as the mass number, then:

A = N + Z

Figure 1. The radius has mass number A = 226, decays to radon with A = 222, and emits a helium nucleus of A = 4. Source: Wikimedia Commons. PerOX

Examples of mass numbers

Here are some examples of mass numbers for well-known elements:

Hydrogen

The most stable and abundant hydrogen atom is also the simplest: 1 proton and one electron. Since the hydrogen nucleus has no neutrons, it is true that A = Z = 1.

Oxygen

An oxygen nucleus has 8 neutrons and 8 protons, therefore A = 16.

Carbon

Life on Earth is based on the chemistry of carbon, a light atom with 6 protons in its nucleus plus 6 neutrons, so A = 6 + 6 = 12.

Uranium

This element, much heavier than the previous ones, is well known for its radioactive properties. The uranium nucleus has 92 protons and 146 neutrons. Then its mass number is A = 92 + 146 = 238.

How to get the mass number?

As mentioned before, the mass number A of an element always corresponds to the sum of the number of protons and the number of neutrons that its nucleus contains. It is also a whole number, but… is there any rule regarding the relationship between the two quantities?

Let's see: all the elements mentioned above are light, except uranium. The hydrogen atom is, as we said, the simplest. It has no neutrons, at least in its most abundant version, and in oxygen and carbon, there are equal numbers of protons and neutrons.

It also happens with other light elements, such as nitrogen, another very important gas for life, which has 7 protons and 7 neutrons. However, as the nucleus becomes more complex and the atoms become heavier, the number of neutrons increases at a different rate.

Unlike the light elements, uranium, with 92 protons, has about 1 ½ times that amount in neutrons: 1 ½ x 92 = 1.5 x 92 = 138.

As you can see, it is quite close to 146, the number of neutrons it has.

Figure 2. Stability curve. Source: F. Zapata.

All of this is evident in the curve in Figure 2. It is a graph of N versus Z, known as the nuclear stability curve. There you can see how light atoms have the same number of protons as neutrons, and how from Z = 20 the number of neutrons increases.

In this way the large atom becomes more stable, since the excess of neutrons decreases the electrostatic repulsion between the protons.

Notation for atoms

A very useful notation that quickly describes the type of atom is the following: the symbol of the element and the respective atomic and mass numbers are written as shown below in this diagram:

Figure 3. Atom notation. Source: F. Zapata.

In this notation, the atoms in the previous examples would be:

Sometimes another more comfortable notation is used, in which only the symbol of the element and the mass number are used to denote the atom, omitting the atomic number. In this way, ¹² ₆ C is written simply as carbon-12, ¹⁶ ₈ O would be oxygen-16, and so on for any element.

Isotopes

The number of protons in a nucleus determines the nature of the element. For example, every atom whose nucleus contains 29 protons is a copper atom, no matter what.

Suppose a copper atom loses an electron for whatever reason, it is still copper. However now it is an ionized atom.

It is more difficult for an atomic nucleus to gain or lose a proton, but in nature it can occur. For example, inside the stars, heavier elements are continuously formed from light elements, since the stellar nucleus behaves like a fusion reactor.

And right here on Earth there is the phenomenon of radioactive decay, in which some unstable atoms expel nucleons and emit energy, transforming into other elements.

Finally, there is the possibility that an atom of a certain element has a different mass number, in this case it is an isotope.

A good example is the well-known carbon-14 or radiocarbon, which is used to date archaeological objects and as a biochemical tracer. It is the same carbon, with identical chemical properties, but with two extra neutrons.

Carbon-14 is less abundant than carbon-12, the stable isotope, and it is also radioactive. This means that over time it decays, emitting energy and particles until it becomes a stable element, which in its case is nitrogen.

Carbon isotopes

Carbon exists in nature as a mixture of several isotopes, the most abundant of which is the aforementioned ¹² ₆ C or carbon-12. And in addition to carbon-14 there is ¹³ ₆ C with an additional neutron.

This is common in nature, for example 10 stable isotopes are known of tin. In contrast, of beryllium and sodium only a single isotope is known.

Each isotope, natural or artificial, has a different rate of transformation. In the same way, it is possible to create artificial isotopes in the laboratory, which are generally unstable and radioactively decay in a very short period of fractions of a second, while others take much longer, as long as the age of the Earth or longer.

Table of natural isotopes of carbon

Carbon isotopes	Atomic number Z	Mass number A	Abundance%
12 6 C	6	12	98.89
13 6 C	6	13	1.11
14 6 C	6	14	Traces

Worked Examples

- Example 1

What is the difference between ¹³ ₇ N and ¹⁴ ₇ N?

Reply

Both are nitrogen atoms, since their atomic number is 7. However, one of the isotopes, the one with A = 13, has one less neutron, while ¹⁴ ₇ N is the most abundant isotope.

- Example 2

How many neutrons are there in the nucleus of a mercury atom, denoted as ²⁰¹ ₈₀ Hg?

Reply

Since A = 201 and Z = 80, and also knowing that:

A = Z + N

N = A - Z = 201 - 80 = 121

And it is concluded that the mercury atom has 121 neutrons.

References

1. Connor, N. What is Nucleon - Structure of Atomic Nucleus - Definition. Recovered from: periodic-table.org.
2. Knight, R. 2017. Physics for Scientists and Engineering: a Strategy Approach. Pearson.
3. Sears, Zemansky. 2016. University Physics with Modern Physics. 14th. Ed. Volume 2.
4. Tippens, P. 2011. Physics: Concepts and Applications. 7th Edition. McGraw Hill.
5. Wikipedia. Mass Number. Recovered from: en.wikipedia.org.