The frequencies for series limit of Balmer and Paschen series are ' $\mathrm{V}_1$ ' and ' $\mathrm{V}_3$ ' respectively. If frequency of first line of Balmer series ' $\mathrm{V}_2$ ' then the relation between $V_1, V_2$ and $V_3$ is

A radio active element has rate of disintegration 8000 disintegrations per minute at a particular instant. After four minutes it becomes 2000 disintegrations per minute. The decay constant per minute is

In Paschen series, wavelength of first line is ' $\lambda_1$ ' and for Brackett series, wavelength of first line is ' $\lambda_2$ ' then ratio $\frac{\lambda_1}{\lambda_2}$ is

The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (i) third to $2^{\text {nd }}$ energy level and (ii) highest energy level to $3^{\text {rd }}$ level is