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

When a hydrogen atom is excited by radiation of wavelength $975 \, \mathring{A}$,the maximum and minimum wavelengths of the emitted radiation are respectively:

The total energy of an electron in the $n^{th}$ orbit of a hydrogen atom is $E_n$. The total energy of an electron in the $n^{th}$ orbit of a $He^+$ ion is .........

What is the ratio of the area of the orbit of an electron in the first excited state to that in the ground state of a hydrogen atom (in $: 1$)?

An electron in a hydrogen atom,after absorbing energy photons,can jump between energy states $n_1$ and $n_2$ $(n_2 > n_1)$. It then returns to the ground state,emitting six different wavelengths in the emission spectrum. The energy of the emitted photons can be equal to,less than,or greater than the absorbed photon energy. Determine $n_1$ and $n_2$.

Obtain an expression for the frequency of radiation emitted when a hydrogen atom de-excites from level $n$ to level $(n-1)$. For large $n$,show that this frequency equals the classical frequency of revolution of the electron in the orbit.