Calculate the ratio of the radius of the $2^{nd}$ and $3^{rd}$ orbit of a hydrogen atom. (Note: $r_n \propto n^2$)

The electronic transitions from $n=2$ to $n=1$ will produce the shortest wavelength in which of the following species? (where $n$ is the principal quantum state)

What is the wavenumber of the photon emitted during transition from the orbit $n=5$ to that of $n=2$ in hydrogen atom (in $cm^{-1}$)?
$\left[R_{H}=109677 \ cm^{-1}\right]$

The ratio of the velocity of an electron in the second orbit of $He^{+}$ to the third orbit of $B^{4+}$ is:

The wavelength of the first line of the Balmer series in the hydrogen spectrum is ................ $\mathring{A}$.

The energy of a photon of wavelength $(\lambda) = 1 \, m$ is (Planck's constant $= 6.626 \times 10^{-34} \, J \, s$,speed of light $= 3 \times 10^8 \, ms^{-1}$)