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. `lambda_(3) = lambda_(1) + lambda_(2)`
B. ` lambda_(3) = ( lambda_(1) lambda_(2))/( lambda_(1) + lambda_(2))`
C. ` lambda_(1) + lambda_(2) + lambda_(3) = 0`
D. ` lambda_(3)^(2) = lambda_(1)^(2) + lambda_(2)^(2)`

Answer

B

Explanation

Let the energy in `A, B` and `C` state be `E_(A).E_(B)` and `E_(C)` then from the figure

`(E_(C) - E_(B)) + (E_(B) - E_(A)) = (E_(C) - E_(A))` or `(hc)/(lambda_(1)) + (hc)/(lambda_(2)) = (hc)/(lambda_(3))`
`rArr lambda_(3) = (lambda_(1)lambda_(2))/(lambda_(1) + lambda_(2))`