Q 12-13-067JEE MainJEE Main 2023 (24 Jan, Shift 1)Medium
Assume that protons and neutrons have equal masses. Mass of a nucleon is $1.6\times10^{-27}\ \text{kg}$ and radius of nucleus is $1.5\times10^{-15}A^{1/3}\ \text{m}$. The approximate ratio of the nuclear density and water density is $n\times10^{13}$. The value of $n$ is ______.
Numerical value type. Enter your answer.
Answer: 11
$$\rho_N=\frac{Am}{\frac43\pi R_0^3A}=\frac{1.6\times10^{-27}}{\frac43\times3.14\times3.375\times10^{-45}}\approx1.13\times10^{17}\ \text{kg m}^{-3}$$
$\dfrac{\rho_N}{\rho_w}=\dfrac{1.13\times10^{17}}{10^3}=11.3\times10^{13}$, so $n\approx11$.
Solution by Sreeraj P, M.Sc Physics