Which among the following electron transitions $(n_2 \rightarrow n_1)$ in a $H$-atom results in the minimum change in its orbit radius $(r_2 - r_1)$?

Explain linear and angular momentum.

The limiting line in the Balmer series of the $H$ spectrum has a frequency of ....... $(R_\infty = 3.29 \times 10^{15} \, cycles/s)$

Rutherford's experiment,which established the nuclear model of the atom,used a beam of

For the Balmer series in the spectrum of $H$ atom,$\bar{v}=R_{H}\left\{\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right\}$,the correct statements among $(I)$ to $(IV)$ are:
$(I)$ As wavelength decreases,the lines in the series converge.
$(II)$ The integer $n_{1}$ is equal to $2$.
$(III)$ The lines of longest wavelength corresponds to $n_{2}=3$.
$(IV)$ The ionization energy of hydrogen can be calculated from wave number of these lines.

Calculate the energy required for the process $He_{(g)}^{+} \rightarrow He_{(g)}^{2+} + e^{-}$. The ionization energy for the $H$ atom in the ground state is $2.18 \times 10^{-18} \, J \, atom^{-1}$.