For a certain atom, there are energy levels A,B,C corresponds to energy values `E_(A)ltE_(B)ltE_(C)`. Choose the correct option if `lambda_(1),lambda_(2),lambda_(3) `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. ` lambda_(3)^(2)=lambda_(1)^(2)+lambda_(2)^(2)`

Answer

B

Explanation

Let energy corresponding to state A, B and C `E_(A),E_(B) and E_(C).`
`" " (E_(C)-E_(B))+(E_(B)-E_(A))=(E_(C )-E_(A))`
`or" " (hc)/(lambda_(1))+(hc)/(lambda_(2))=(hc)/(lambda_(3))rArrlambda_(3)=(lambda_(1)lambda_(2))/(lambda_(1)+lambda_(2))`