A nucleus of mass number \(A\) has an average mass per nucleon \(m\). Its radius is given by \(R_0 A^{1/3}\), where \(R_0\) is a constant. The average mass density of the nucleus will be:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{3m}{4\pi R_0^{3}}\)
Density is mass divided by volume. A nucleus of A nucleons has mass Am, and its radius is \( R = R_0A^{1/3} \), so its volume is proportional to A.
\( \displaystyle V = \frac{4}{3}\pi R^{3} = \frac{4}{3}\pi R_0^{3}A \)
\( \displaystyle \rho = \frac{Am}{\frac{4}{3}\pi R_0^{3}A} \)
\( \displaystyle \rho = \frac{3m}{4\pi R_0^{3}} \)
The mass number cancels, so nuclear density is the same for all nuclei.