Using Bohr's model, the orbital period of electron in hydrogen atom in the $$\mathrm{n}^{\text {th }}$$ orbit is $$\left(\varepsilon_0=\right.$$ permittivity of vacuum, $$\mathrm{h}=$$ Planck's constant, $$\mathrm{m}=$$ mass of electron, $$\mathrm{e}=$$ electronic charge)

The wave number of the last line of the Balmer series in hydrogen spectrum will be

(Rydberg's constant $$=10^7 \mathrm{~m}^{-1}$$ )

The half life of a radioactive substance is 30 minute. The time taken between 40% decay and 85% decay of the same radioactive substance is

The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (i) second to first energy level and (ii) highest energy level to second energy level is