When a hydrogen sample in the ground state is bombarded with electrons,what potential is required to accelerate the electrons so that the first Brackett line is emitted? $(eV)$

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.

Assertion : For Balmer series of hydrogen spectrum,the value $n_1 = 2$ and $n_2 = 3, 4, 5...$
Reason : The value of $n$ for a line in Balmer series of hydrogen spectrum having the highest wavelength is $4$ and $6$.

Calculate the ratio of the radius of the $2^{nd}$ and $3^{rd}$ orbit of a hydrogen atom. (Note: $r_n \propto n^2$)

If the energy of the first orbit of $He^{+}$ is $-54.4 \, eV$,then the energy of the second orbit will be ............. $eV$.

Which one of the following is considered as the main postulate of Bohr’s model of atom?