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

5.1.2 The Nucleus

Objective

Understand the relationship between the nucleon number (mass number) and the relative mass of a nucleus.

Key Concepts

• Nucleons: The particles that make up the nucleus – protons and neutrons.
• Mass number (A): The total number of nucleons in a nucleus (protons + neutrons).
• Relative atomic mass (atomic mass unit, u): The mass of a particle relative to 1/12 the mass of a carbon‑12 atom.

Relative Masses of Sub‑Atomic Particles

Relationship Between Nucleon Number and Relative Mass

The mass of a nucleus is essentially the sum of the masses of its constituent protons and neutrons. Because the mass of an electron is negligible compared with nucleons, the relative mass of a nucleus can be approximated by the nucleon number:

\$m_{\text{nucleus}} \approx A\ \text{u}\$

where A is the nucleon (mass) number.

Why the Approximation Works

• Protons and neutrons have almost the same mass (≈1 u each).
• The electron’s mass contributes less than 0.05 % to the total atomic mass and is therefore ignored in the approximation.
• Binding energy (the energy required to separate the nucleus into individual nucleons) reduces the actual mass slightly, according to Einstein’s relation \$E=mc^2\$. This reduction is called the mass defect and is typically a few parts per thousand.

Worked Example

Find the relative mass of a nitrogen‑14 nucleus.

1. Identify the nucleon number: \$A = 14\$ (7 protons + 7 neutrons).
2. Apply the approximation: \$m_{\text{N‑14}} \approx 14\ \text{u}\$.
3. Consider the mass defect (optional). The actual measured mass is about \$13.999\ \text{u}\$, showing a tiny reduction due to binding energy.

Common Misconceptions

• “All nuclei have exactly the same mass as their nucleon number.” – In reality, binding energy causes a small mass defect.
• “Electrons contribute significantly to atomic mass.” – Their mass is negligible compared with nucleons.
• “Protons and neutrons have identical masses.” – Their masses differ slightly (1.0073 u vs 1.0087 u), but the difference is small enough for the approximation.

Quick Check Questions

1. What is the nucleon number of an oxygen‑16 atom?
2. Using the approximation, what is the relative mass of a calcium‑40 nucleus?
3. Explain why the measured mass of a carbon‑12 nucleus is exactly 12 u, while other nuclei show a slight mass defect.