In Geiger-Marsden experiment, the number of scattered $\alpha$-particles $N(\theta)$ is plotted as a function of scattering angle $\theta$. Which of the following options represents the correct plot?

In the first excited state of hydrogen atom, the energy of its electron is -3.4 eV . The radial distance of the electron from the hydrogen nucleus in this case is approximately:

(Take $1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}, \mathrm{e}=1.6 \times 10^{-19} \mathrm{C}$ and $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{~N} \mathrm{~m}^2 / \mathrm{C}^2$ )

Four statements are given ( $A$ is mass number):

A. The volume of a nucleus is proportional to $A^{1 / 3}$.

B. The volume of a nucleus is proportional to $A$.

C. The difference in mass of an atom and its nucleus is called the mass defect.

D. The difference in mass of a nucleus and its constituents is called the mass defect.

Choose the correct answer from the options given below:

An unknown nucleus has a nuclear density of $2.29 \times 10^{17} \mathrm{~kg} / \mathrm{m}^3$ and mass of $19.926 \times 10^{-27} \mathrm{~kg}$. Its mass number $A$ is approximately:

(Take $R_0=1.2 \times 10^{-15} \mathrm{~m}, 4 \pi=12.56$ )