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Transition between three energy energy ...

Transition between three energy energy levels in a particular atom give rise to three Spectral line of wevelength , in increasing magnitudes. `lambda_(1), lambda_(2)` and `lambda_(3)`. Which one of the following equations correctly ralates `lambda_(1), lambda_(2)` and `lambda_(3)`?

Text Solution

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`(1)/(lambda_(1)) = R_oo Z^(2) [(1)/(2^(2)) - (1)/(3^(2))]` (i)
`(1)/(lambda_(2)) = R_oo Z^(2) [(1)/(1^(2)) - (1)/(2^(2))]` (ii)
`(1)/(lambda_(3)) = R_oo Z^(2) [(1)/(1^(2)) - (1)/(3^(2))]` (iii)
On adding (i) and (ii), we get
`(1)/(lambda_(1)) + (1)/(lambda_(2)) = R_oo Z^(2) [(1)/(1^(2)) - (1)/(3^(2))]`
Thus,`(1)/(lambda_(1)) + (1)/(lambda_(2)) = (1)/(lambda_(3))`
`lambda_(3) = (lambda_(1) lambda_(2))/(lambda_(1) + lambda_(2))`
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