Supposing the electron is present in the $4^{th}$ energy level of $H$ atom. When the electron returns to the ground state,the possible transitions would be:

The ratio of the radii of two Bohr orbits of a hydrogen atom is $4:1$. What are their designations?

The value of Rydberg constant $\left(R_H\right)$ is $2.18 \times 10^{-18} \ J$. The velocity of an electron having mass $9.1 \times 10^{-31} \ kg$ in Bohr's first orbit of a hydrogen atom $= \dots \dots \dots \times 10^5 \ ms^{-1}$ (nearest integer).

The ionization energy of $He^+$ is $19.6 \times 10^{-18} \ J \ atom^{-1}$. What is the energy of the first stationary state $(n = 1)$ of $Li^{2+}$?

The number of photons emitted by a monochromatic (single frequency) infrared range finder of power $1 \, mW$ and wavelength of $1000 \, nm$,in $0.1 \, s$ is $x \times 10^{13}$. The value of $x$ is ..... .
(Nearest integer)
$(h=6.63 \times 10^{-34} \, J \, s, c=3.00 \times 10^{8} \, m \, s^{-1})$

Supposing the electron of the $H$ atom is present in the $L$ shell. If it liberates $10.2 \ eV$,what is the energy of the system? ............. $eV$