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Energy levels A, B, C of a certain atom ...

Energy levels `A, B, C` of a certain atom corresponding to increasing values of energy i.e., `E_(A) lt E_(B) lt E_(C)`. If `lambda_(1), lambda_(2), lambda_(3)` are the wavelengths of radiations corresponding to the transitions `C` to `B, B` to `A` and `C` to `A` respectively, which of the following statements is correct?

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)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let the enegry in `A, B` and `C` state be `E_(A), E_(B)` and `E_(C)`. The form the figure

`(E_(C) - E_(B)) + (E_(B) - E_(A)) = (E_(C) - E_(A))`
or `(hc)/(lambda_(1)) + (hc)/(lambda_(2)) = (hc)/(lambda_(3))`
`rArr lambda_(3) = (lambda_(1)lambda_(2))/(lambda_(1) + lambda_(2))`
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