The half life of a radioactive nucleus is 50 days. The time invertal (t₂ $$-$$ t₁) between the time t₂ when $${2 \over 3}$$ of it has decayed and the time t₁ when $${1 \over 3}$$ of it had decayed is

The transition from the state n = 3 to n = 1 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from

An electron of a stationary hydrogen atom passes from the fifth energy level to the ground level. The velocity that the atom acquired as a result of photon emission will be

Electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state. The ratio of the wavelengths $$\lambda $$₁ : $$\lambda $$₂ emitted in the two cases is