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In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is λ. If an electron jumps from N-shell to the L-shell, the wavelength of emitted radiation will be:

1. 25/16 λ
2. 27/20 λ
3. 16/25 λ
4. 20/27 λ

Correct answer: 20/27 λ

Solution

For M->L (3->2): 1/lambda = R(1/4 - 1/9) = 5R/36. For N->L (4->2): 1/lambda' = R(1/4 - 1/16) = 3R/16. So lambda'/lambda = (5/36)/(3/16) = 80/108 = 20/27. The emitted wavelength is (20/27) lambda.

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