Question

State any two properties of a nucleus.

Hint:

The density of nuclear matter is constant because the nucleus’s radius increases with \(A^{1/3}\), while its mass is proportional to \(A\).

Answer 1

(a) Properties of a Nucleus:
1. The nucleus contains protons and neutrons, collectively called nucleons.
2. The nucleus has a positive charge due to the presence of protons.
(b) Nuclear Density: - The nucleus is much denser than the atom because most of the mass of an atom is concentrated in its tiny nucleus, whereas the atom's size includes the much larger electron cloud.
(c) Density of Nuclear Matter: - The volume of a nucleus is proportional to \(A\), where \(A\) is the mass number. The radius \(R\) of a nucleus is given by: \[ R = R_0 A^{1/3} \] - The density of the nucleus is: \[ \rho = \frac{\text{Mass of Nucleus}}{\text{Volume of Nucleus}} = \frac{m_N A}{\frac{4}{3} \pi R^3} = \frac{m_N}{\frac{4}{3} \pi R_0^3} \] - Since \(R_0\) and \(m_N\) are constants, the density is the same for all nuclei.