If the radius of a hydrogen atom in its first orbit is $a_{0}$,then its radius in the third excited state is . . . . . . . (in $a_{0}$)

Neglecting the reduced mass effect,which optical transition in the $He^+$ spectrum has the same wavelength as the first Lyman transition of hydrogen ($n = 2$ to $n = 1$)?

Find the ratio of the area of the orbit of the first excited state to the ground state in a hydrogen atom.

The magnetic moment of an electron due to its orbital motion is proportional to (where $n$ is the principal quantum number).

In a hydrogen-like atom,an electron makes a transition from an energy level with quantum number $n$ to another with quantum number $(n - 1)$. If $n >> 1$,the frequency of radiation emitted is proportional to:

Using the formula for the radius of the $n^{th}$ orbit $r_n = \frac{n^2 h^2 \epsilon_0}{\pi m Z e^2}$,derive an expression for the total energy of an electron in the $n^{th}$ Bohr orbit.