Energy levels A,B,C of a certain atom correspond to increasing values of energy i.e., `E_(A) lt E_(B)ltE_(C)`. If `lambda_(1), lambda_(2), and lambda_(3)` are the wavelength 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. `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

Energy levles of A,B and C can be correlated below
`E_(CA)=E_(CB)+E_(BA)`
`rArr (hc)/(lambda_3)=(hc)/(lambda_1)+(hc)/(lambda_2)`
`rArr (1)/(lambda_3)=(1)/(lambda_1)+(1)/(lambda_2)or lambda_(3)=(lambda_1lambda_2)/(lambda_1+lambda_2)`