If the frequency of radiation emitted for the electron transition from an excited state to ground state of hydrogen atom is $\frac{3 X}{4} \ Hz$,the frequency of radiation absorbed for the electron transition from the above excited state to the next immediate excited state in $Hz$ is:

The ionization energy of a hydrogen atom is $13.6 \ eV$. The energy required to ionize a hydrogen atom in its second excited state is ........... $eV$.

When electromagnetic radiation of wavelength $310 \ nm$ falls on the surface of a metal having work function $3.55 \ eV$,the velocity of photoelectrons emitted is $x \times 10^5 \ ms^{-1}$. The value of $x$ is (Nearest integer). Given: $m_{e} = 9 \times 10^{-31} \ kg$,$h = 6.63 \times 10^{-34} \ J \cdot s$,$c = 3 \times 10^8 \ m/s$,$1 \ eV = 1.6 \times 10^{-19} \ J$.

Ratio of velocities of electrons of hydrogen atom in $1^{st}$,$2^{nd}$,$3^{rd}$ orbit is

If the energies of two light radiations $E_1$ and $E_2$ are $25 \ eV$ and $100 \ eV$ respectively,then their respective wavelengths $\lambda_1$ and $\lambda_2$ would be in the ratio $\lambda_1: \lambda_2=$

The number of maximum possible different spectral lines obtained in the Balmer series,when an electron makes a transition to the ground state from the $5^{th}$ excited state in a sample of hydrogen atoms,is: