Question

. What is the ratio of nuclear densities of two nuclei having mass numbers in the ratio 1:8? 

Answer 1

We have:

$$\frac{m_1}{m_2}=\frac{\rho_1 V_1}{\rho_2V_2}=\frac18.$$

re-write in terms of radii:

$$\frac{\rho_1r_1^3}{\rho_2r_2^3}=\frac{\rho_1[R_0(m_1)]^{1/3}}{\rho_2[R_0(m_2)]^{1/3}}=\frac18,\\\space\\ \frac{\rho_1·1^{1/3}}{\rho_2·8^{1/3}}=\frac18,\\\space\\ \frac{\rho_1}{\rho_2}=\frac14.$$