The total number of spectral lines observed when an electron returns from the $6^{th}$ shell to the $2^{nd}$ shell in a hydrogen atom is:

In the hydrogen spectrum,a line corresponds to a transition from the $3^{rd}$ to the $5^{th}$ orbit. Identify the series to which this transition belongs.

What is the ratio of the wave number of the first line (lowest energy line) of the Balmer series of the $H$ atomic spectrum to the first line of its Brackett series?

If the radius of the hydrogen atom is $53 \, pm$, the radius of the $He^{+}$ ion is closest to $...... \, pm$.

$A$ photon of wavelength $4 \times 10^{-7} \, m$ strikes on a metal surface. The work function of the metal is $2.13 \, eV$. Calculate:
$(i)$ The energy of the photon in $eV$.
$(ii)$ The kinetic energy of the emission in $eV$.
$(iii)$ The velocity of the photoelectron in $ms^{-1}$ ($1 \, eV = 1.6020 \times 10^{-19} \, J$,mass of electron $m = 9.10939 \times 10^{-31} \, kg$).

If the velocity of an electron in the $n^{th}$ orbit of a Bohr atom is $v$,what is the value of $n$?