1.

The energy states A, B and C having energy E_(A)ltE_(B)ltE_(C). If the transition CtoB,BtoA and CtoAhave the corresponding wavelength lamda_(1),lamda_(2) and lamda_(3) espectively, then which of following relationship is obtained ?

Answer»

`lamda_(1)+lamda_(2)+lamda_(3)=0`
`lamda_(3)^(2)=lamda_(1)^(2)+lamda_(2)^(2)`
`lamda_(3)=(lamda_(1)lamda_(2))/(lamda_(1)+lamda_(2))`
`lamda_(3)=lamda_(1)+lamda_(2)`

Solution :`E_(A)ltE_(B)ltE_(C)`

For TRANSITION `CTOB`
`E_(C)-E_(B)=(hc)/(lamda_(1))"".......(1)`
For transition `BtoA`
`E_(B)-E_(A)=(hc)/(lamda_(2))"".......(2)`
Adding equation (1) and (2),
`E_(C)-E_(A)=(hc)/(lamda_(1))-(hc)/(lamda_(2))"".......(3)`
Now for transition `CTOA`.
`E_(C)-E_(A)=(hc)/(lamda_(3))"".......(4)`
`:.` From equation (3) and (4),
`(hc)/(lamda_(3))=(hc)/(lamda_(1))+(hc)/(lamda_(2))`
`:.(1)/(lamda_(3))=(1)/(lamda_(1))+(1)/(lamda_(2))`
`:.lamda_(3)=(lamda_(1)lamda_(2))/(lamda_(1)+lamda_(2))`


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