Transition between three energy energy levels in a particular atom give rise to three Spectral line of wevelength , in increasing magnitudes. `lambda_(1), lambda_(2)` and `lambda_(3)`. Which one of the following equations correctly ralates `lambda_(1), lambda_(2)` and `lambda_(3)`?

Options

A. `lamda_1 = lamda_2 - lamda_3`
B. `lamda_1 = lamda_3 - lamda_2`
C. `(1)/(lamda_1) = (1)/(lamda_2) + (1)/(lamda_3)`
D. `(1)/(lamda_1) = (1)/(lamda_3) - (1)/(lamda_2)`

Answer

A

Explanation

(a) `N = N_0 e^(-lamda t)` or `e^(lamda t) = (N_0)/(N)`
or `lamda t = log_e ((N_0)/(N))` or `t = (1)/(lamda) log_e ((N_0)/(N))`
or `t = (t_alpha t_beta)/(t_alpha + t_beta) log_e ((4)/(1))`
or `t = 2.303 xx (t_alpha t_beta)/(t_alpha + t_beta) log_10 4`
or `t = 2 xx 2.303 xx (t_alpha t_beta)/(t_alpha + t_beta) log_10 2`
or `t = (2 xx 2.303 xx 0.3010 xx 1620 xx 405)/(1620 + 405)` years
`=449.2` years.