Question

What is the meaning of nucleon? What is the mass number of nucleus? Write down the relation between mass number and radius of nucleus and show that the density of nucleus does not depend on mass number.

Hint:

Nuclear density remains constant for all nuclei, regardless of their mass number, as the mass and volume both scale proportionally with \( A \).

Answer 1

Nucleon: A nucleon refers to either a proton or a neutron in the nucleus of an atom. Nucleons are the building blocks of the nucleus.
Mass Number of Nucleus: The mass number of a nucleus is the total number of nucleons (protons and neutrons) present in the nucleus. It is represented by \( A \), where \( A = Z + N \),
- \( Z \) is the number of protons,
- \( N \) is the number of neutrons.
Relation Between Mass Number and Radius of Nucleus:
The radius of a nucleus is given by the empirical formula: \[ R = R_0 A^{1/3} \] Where: - \( R_0 \) is a constant, approximately \( 1.2 \, \text{fm} \),
- \( A \) is the mass number of the nucleus.
Density of Nucleus: The density of the nucleus is defined as the mass per unit volume. The volume of the nucleus is proportional to \( R^3 \), and since \( R \propto A^{1/3} \), the volume is proportional to \( A \). Hence, the mass of the nucleus is proportional to \( A \), and the density of the nucleus becomes: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \propto \frac{A}{A} = \text{constant} \] This shows that the density of the nucleus is independent of the mass number \( A \).