Question

Since the nucleus is approximately spherical with \[R = R_0 A^{1/3}\], its volume \[V = \frac{4}{3}\pi R^3\] is proportional to:

Options

• \[A^{3}\]

• \[A^{1/3}\]

• \[A^{2}\]

• \[A\]

Answer 1

Substituting \[R = R_0 A^{1/3}\] into \[V = \frac{4}{3}\pi R^3\] gives \[V = \frac{4}{3}\pi R_0^3 A\]. Thus, the nuclear volume becomes proportional to \[A\] and increases nearly in direct proportion to the mass number.