The four lowest energy levels of the $H$ atom are shown in the figure. The number of emission lines will be ...... .

The wavelength of the radiation emitted,when in a hydrogen atom an electron falls from infinity to stationary state $n=1$,would be ............... $nm$ (Rydberg constant $= 1.097 \times 10^7 \ m^{-1}$)

Emission transitions in the Paschen series end at orbit $n=3$ and start from orbit $n$ and can be represented as $\nu = 3.29 \times 10^{15} \, Hz \left(\frac{1}{3^2} - \frac{1}{n^2}\right)$. Calculate the value of $n$ if the transition is observed at $1285 \, nm$. Find the region of the spectrum.

The ratio of the energy of a photon of $2000 \ \mathring{A}$ wavelength radiation to that of $4000 \ \mathring{A}$ radiation is

Find out the distance between the $2^{nd}$ and $3^{rd}$ orbit of the $H$-atom $:-$

Consider an electron moving in the first Bohr orbit of a $He^{+}$ ion with a velocity $v_1$. If it is allowed to move in the third Bohr orbit with a velocity $v_3$, then indicate the correct $v_3: v_1$ ratio.