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

The Balmer series in the hydrogen spectrum corresponds to the transition from $n_1 = 2$ to $n_2 = 3, 4, ...$ This series lies in the visible region. Calculate the wave number of the line associated with the transition in the Balmer series when the electron moves to the $n = 4$ orbit. $(R_H = 109677 \ cm^{-1})$

In the atomic spectrum of hydrogen, the wavelengths of the spectral lines corresponding to electronic transitions $(i)$ $n=4$ to $n=2$ and $(ii)$ $n=3$ to $n=1$ are $\lambda_1$ and $\lambda_2$ $\mathring{A}$ respectively. The value of $(\lambda_1-\lambda_2)$ (in cm) is ($R_H$ = Rydberg constant)

If the wave number of radiation emitted for the electron transition from an excited state to ground state of hydrogen is $\frac{5x}{36} \ m^{-1}$,the wave number of radiation absorbed for the electron transition from the above excited state to the next immediate excited state in $m^{-1}$ is:

The dual nature of photons is described by:

The frequency and energy of a photon with a wavelength of $4000 \ \mathring{A}$ are respectively.......