What is the energy of an electron in the stationary state corresponding to $n=2$?

State whether the following statements are true or false:
$(i)$ In Rutherford's atomic model,the Coulombic forces between the nucleus and electrons are mathematically similar to the gravitational forces $F = G \frac{m_1 m_2}{r^2}$.
$(ii)$ Out of every $20000$ $\alpha$-particles,$\sim 10$ particles bounce back after hitting the gold foil.
$(iii)$ In Rutherford's experiment,a zinc sulfide $(ZnS)$ fluorescent screen is placed around the gold foil.
$(iv)$ Rutherford's $\alpha$-particle scattering experiment is related to the size of the atomic nucleus.

In which one of the following pairs of experimental observations and phenomena does the experimental observation correctly account for the phenomenon?

In Bohr's model of the atom,when an electron jumps from $n=1$ to $n=3$,how much energy will be absorbed?

When an electron in a hydrogen atom jumps from an infinite state to the first stationary state,the wavelength of the emitted radiation will be ...... (Rydberg constant = $1.097 \times 10^7 \ m^{-1}$):

The difference between the radii of $3^{rd}$ and $2^{nd}$ orbit of $H$ atom is $x \text{ pm}$. The difference between the radii of $4^{th}$ and $3^{rd}$ orbit of $Li^{2+}$ ion is $y \text{ pm}$. The ratio $y:x$ is equal to: