For a certain atom, there are energy levels A, B, C corresponds to energy values `E_A lt E_B lt E_C` . Choose the correct option if `lambda_1, lambda_2, lambda3` are the wavelength of radiations corresponding to the transition from C to B, B to A and C to A respectively.

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. `3lambda_2=lambda_3+2lambda_2`

Answer

B

Explanation

The energy difference between levels C and A will equal to the sum of energy difference between levels C & B levels B&A.
`E_B-E_A = (hc)/(lambda_1)`
`E_C-E_B = (hc)/(lambda_2)`
`E_C-E_A = (hc)/(lambda_3)`
or` 1/lambda_3 =1/lambda_1 + 1/lambda_2`
`lambda_3 =(lambda_1 lambda_2)/(lambda_1+lambda_2)`