Ratio of longest wave lengths corresponding to Lyman and Balmer series in hydrogen spectrum is

The half life of a radioactive isotope 'X' is 20 years. It decays to another element 'Y' which is stable. The two elements 'X' and 'Y' were found to be in the ratio 1 : 7 in a sample of a given rock. The age of the rock is estimated to be

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