Energy levels A B C of a certain atom corresponding to increasing value of energy i.e., E_A E_B E_C If ` lambda _1, lambda_2`, and ` 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 statement is correct
.

Options

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

Answer

D

Explanation

Data :

Using Bohr's spectral condition for emission of radiation
we have , `E_C - E_B = hv_1 = (hc)/(lamda_1) " " …(1)`
`E_B-E_A = (hc)/(lamda_2) " " …(2)`
`E_C-E_A = (hc)/(lamda_3) " "…(3)`
But `E_C - E_A = (E_C - E_B) +(E_B-E_A)`
`therefore (hc)/(lamda_3) = (hc)/(lamda_1) +(hc)/(lamda_2)`
`therefore 1/lamda_3 = 1/lamda_1 + 1/ lamda_2 = (lamda_1 + lamda_2)/(lamda_1lamda_2)`
`therefore lamda_3 = (lamda_1lamda_2)/(lamda_1+lamda_2)`