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

Options

A. `lamda_(3) = lamda_(1) + lamda_(2)`
B. `lamda_(3)= (lamda_(1) lamda_(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

Since, `(E_(C)- E_(B)) + (E_(B)- E_(A)) = (E_(C)- E_(A))`
`rArr (hc)/(lamda_(1)) + (hc)/(lamda_(2))= (hc)/(lamda_(3))`
`rArr lamda_(3)= (lamda_(1)lamda_(2))/(lamda_(1) + lamda_(2))`