The energies of energy levels A, B and C for a given atom are in the sequence `E_(A)ltE_(B)ltE_(C)`. If the radiations of wavelength `lambda_(1), lambda_(2)` and `lambda_(3)` are emitted due to the atomic transitions C to B, B to A and C to A respectively then which of the following relations is correct :-

Options

A. `lambda_(1)+lambda_(2)+lambda_(3)=0`
B. `lambda_(3)=lambda_(1)+lambda_(2)^(2)`
C. `lambda_(3)=lambda_(1)+lambda_(2)`
D. `lambda_(3)=(lambda_(1)lambda_(2))/(lambda_(1)+lambda_(2))`

Answer

D

Explanation

`E_(C)-E_(B)=(hc)/(lambda_(1))" "…(i)`
`E_(B)-E_(A)=(hc)/(lambda_(2)) " "…(ii)`
`E_(C)-E_(A)=(hc)/(lambda_(3))" "…(iii)`
add equation (1) and (2)
`E_(C)-E_(A)=hc((1)/(lambda_(1))+(1)/(lambda_(2)))`
put in equatin (3) ltbgt `hc((1)/(lambda_(1))+(1)/(lambda_(2)))=(hc)/(lambda_(3))`
`(1)/(lambda_(3))=(lambda_(1)+lambda_(2))/(lambda_(1)lambda_(2))implieslambda_(3)=(lambda_(1)lambda_(2))/(lambda_(1)+lambda_(2))`