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

In hydrogen atom in its ground state, the first Bohr orbit has radius ' $\mathrm{r}_1$ '. When the atom is raised to one of its excited states, the electrons orbital velocity becomes one-third. The radius of that orbit is

A radioactive element has rate of disintegration 9000 disintegration per minute at a particular instant. After two minutes it becomes 3000 disintegration per minute. The decay constant per minute is