Choose the correct statements from the following based on the properties of atomic nucleus.
I. Radius of a nucleus of man no. A depends on its mass number as $R \propto A^3$
II. Radius of nucleus and mass number are related as $R \propto A^{\frac{1}{3}}$
III. Density of nuclei is always a constant
IV. Density of nuclei depends on its mass number A
V. Density of nuclei depends on its size, volume
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → II and III only
Sol. We known, volume of nucleus $V \propto A$
∴ $\frac{4}{3} \pi R^3 \propto A$
∴ $R \propto A^{1 / 3}$
Now, density of nucleus $\rho=\frac{M}{V}=\frac{A}{\frac{4}{3} \pi\left(R_0 A^{1 / 3}\right)^3}$
$\rho=\frac{1}{\frac{4}{3} \pi R_0^3} \Rightarrow$ constant
Thus density of nucleus is constant