What is the energy associated with the first orbit of $He^{+}$?

Which transition in a $H$ atom has the same wavelength as the transition from $n = 4$ to $n = 2$ in a $He^{+}$ ion?

If the binding energy of electrons in a metal is $250 \ kJ \ mol^{-1}$,what should be the threshold frequency of the striking photons in order to free an electron from the metal surface?

For any given series of spectral lines of atomic hydrogen,let $\Delta \bar{\nu} = \Delta \bar{\nu}_{\max} - \Delta \bar{\nu}_{\min}$ be the difference in maximum and minimum wavenumbers in $cm^{-1}$. The ratio $\Delta \bar{\nu}_{\text{Lyman}} / \Delta \bar{\nu}_{\text{Balmer}}$ is

Assertion : The radius of the first orbit of hydrogen atom is $0.529 \ \mathring{A}$.
Reason : Radius of each circular orbit $(r_n) = 0.529 \ \mathring{A} \ (n^2/Z)$,where $n = 1, 2, 3$ and $Z =$ atomic number.

In the Rutherford experiment,if light atoms are used instead of heavy elements,what change is observed in the results?