1. Use the nuclear radius relation

   For a nucleus, $R = R_0 A^{1/3}$ where $R_0$ is a constant.

2. Write the nuclear mass

   Mass of the nucleus is approximately proportional to its mass number: $M \propto A$ More specifically, $M \approx A m_n$, where $m_n$ is the nucleon mass.

3. Find the nuclear volume

   Assuming the nucleus is spherical, $V = \frac{4}{3}\pi R^3$ Substituting $R = R_0 A^{1/3}$, $V = \frac{4}{3}\pi (R_0 A^{1/3})^3 = \frac{4}{3}\pi R_0^3 A$ So, $V \propto A$

4. Compute the density

   Density is $\rho = \frac{M}{V}$ Since both $M \propto A$ and $V \propto A$, $\rho \propto \frac{A}{A} = \text{constant}$

5. Conclusion

   The mass density of a nucleus is independent of $A$.

6. Check options

   • A: $A^{2/3}$ — Incorrect
   • B: Independent of $A$ — Correct
   • C: $A^3$ — Incorrect
   • D: $A^{1/3}$ — Incorrect

Therefore, the correct answer is: $\boxed{\text{B}}$