A hydrogen-like atom emits rediationof frequency `2.7 xx 10^(15)` Hz` when if makes a transition from `n = 2 to n = 1`. The frequency emitted in a transition from `n = 3 to n = 1` will be

Options

A. `1.8 xx 10^15 Hz`
B. `3.2 xx 10^15 Hz`
C. `4.7 xx 10^5 Hz`
D. `6.9 xx 10^15 Hz`.

Answer

D

Explanation

(d) `N = N_0 e^(-lamda t)`
`(N_0)/(N) = e^(lamda t)` or `lamda t = log_e ((N_0)/(N))`
or `t = (1)/(lamda) log_e ((N_0)/(N))`or `t= (T)/(0.693) log_e ((N_0)/(N))`
=`(5700)/(0.693) xx 2.303 log_10 ((4)/(1))`
=`(2 xx 5700 xx 2.303)/(0.693) log_e 2`
=`(2 xx 5700 xx 2.303 xx 0.3010)/(0.693) years`
=`11403 years`.