Energy levels A,B and C of a certain atom correspond to increasing values of energy i.e. `E_(A) lt E_(B) lt E_(C)` .If `lamda_(1),lamda_(2),lamda_(3)` are the wavelengths of radiation corresponding to transition C to B,B to A and C to A respectively, which of the following statements is correct ?

Options

A. `lamda_3 = lamda_1 + lamda_2`
B. `lamda_3 = (lamda_1lamda_2)/(lamda_1 +lamda_2)`
C. `lamda_1 + lamda_2 + lamda_3 = 0`
D. `lamda_3^2 = lamda_1^2 + lamda_2^2`

Answer

B

Explanation

`(E_2-E_1) = hv = (hc)/(lamda)`
` therefore (hc)/(lamda_1) = (E_C - E_B) , (hc)/(lamda_2) = (E_B - E_A)`
and `(hc)/(lamda_3) = (E_C - E_A)`
Now,
`(E_C - E_A) = (E_C - E_B) + (E_B - E_A)`
or `(hc)/(lamda_3) = (hc)/(lamda_1) + (hc)/(lamda_2) " or " (1)/(lamda_3) = (1)/(lamda_1) + (1)/(lamda_2)`
` therefore (1)/(lamda_3) = (lamda_1 + lamda_2)/(lamda_1 lamda_2) " or " lamda_3 = (lamda_1 lamda_2)/(lamda_1 + lamda_2)`