For a $H$ atom,the energy transition from $n = 1$ to $n = 2$ is $10.2 \ eV$. What will be the energy for the same transition in $Be^{3+}$ ion?

Rutherford's $\alpha$-particle scattering experiment eventually led to the conclusion that

The ratio of the radius of the second orbit of hydrogen to the third orbit of $Li^{+2}$ is .... ($H$ atomic number = $1, Li$ atomic number = $3$)

State whether the following statements are true or false:
$(i)$ When an electron in a hydrogen atom returns from the third excited state to the ground state,it emits frequencies corresponding to lines in the Lyman,Balmer,and Paschen series.
$(ii)$ When an electron in a hydrogen atom returns from the third excited state to the ground state,it emits radiation with wavelengths corresponding to the Pfund series,which has very high frequencies.

Circumference of the first orbit of hydrogen atom is given by the formula :

The energy required to release $1$ electron from $He^{+}$ is $............$ $eV$.