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 correspnding to the transitions `C` to `B, B` to `A` and `C` to `A` respectively, which o fthe following statements 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

`v_("Balmer") = (c )/(lambda_(max)) = Rc [(1)/((2)^(2)) - (1)/((3)^(2))] = (5RC)/(36)`
or `(hc)/(lambda_(1)) + (hc)/(lambda_(2)) = (hc)/(lambda_(3)) lambda_(3) = (lambda_(1)lambda_(2))/(lambda_(1)+lambda_(2))`