Know the relationship between the nucleon number and the relative mass of a nucleus

What is a nucleus?

The nucleus is the tiny, dense core of an atom, made up of protons (positively charged) and neutrons (neutral). Think of it as a super‑compact Lego tower where each block is a nucleon. The tower’s height (number of blocks) is called the nucleon number (A).

Nucleon number (A) and relative mass

The nucleon number is simply the total count of protons and neutrons:

$A = Z + N$

Where $Z$ = number of protons and $N$ = number of neutrons.

However, the relative mass (often called the mass number) is not exactly equal to A because some mass is converted into binding energy when nucleons stick together.

Analogy: Imagine you glue Lego blocks together. The glued tower weighs a little less than the sum of the individual blocks because a tiny amount of mass is released as energy (like a small spark).

Mass defect and binding energy

The mass defect (Δm) is the difference between the sum of the masses of the individual nucleons and the actual mass of the nucleus:

$Δm = (Z m_p + N m_n) - m_{\text{nucleus}}$

Using Einstein’s equation $E = Δm c^2$, this missing mass becomes binding energy that holds the nucleus together.

Because the binding energy per nucleon is usually a few MeV, the relative mass is slightly less than A. For most light nuclei, the difference is tiny, but it becomes noticeable for heavier elements.

Example: Helium‑4

• Protons $Z = 2$
• Neutrons $N = 2$
• Nucleon number $A = 4$
• Actual mass $m_{\text{He-4}} = 4.002602\,u$
• Relative mass (mass number) $≈ 4.0000$

Notice the tiny difference: $Δm ≈ 0.002602\,u$, which corresponds to about 28 MeV of binding energy.

Table of common isotopes

Notice how the measured mass is always a little less than the integer A, especially for heavier nuclei.

Exam Tips 📝

1. Remember: Relative mass ≈ nucleon number, but always account for the small mass defect.
2. When given a problem, first calculate $A = Z + N$; then, if asked for relative mass, note that it is usually rounded to the nearest whole number unless a precise value is required.
3. Use the formula $Δm = (Z m_p + N m_n) - m_{\text{nucleus}}$ if the question asks for mass defect or binding energy.
4. Check units: mass defect is often expressed in atomic mass units (u) or MeV/$c^2$.
5. Practice converting between mass defect and binding energy using $E = Δm c^2$ (1 u ≈ 931.5 MeV/$c^2$).