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An electron from various excited states ...

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let `lambda_(n),lambda_(g)` be the de Broglie wavelength of the electron in the `n^(th)` state and the ground state respectively. Let `^^^_(n)` be the wavelength of the emitted photon in the transition from the `n^(th)` state to the ground state. For large n, (A, B are constants)

A

`.^^_(n)^(2) approx A + Blambda_(n)^(2)`

B

`.^^_(n)^(2)approx lambda`

C

`.^^_(n)approx A+B/(lambda_(n)^(2))`

D

`.^^_(n)approx A+Blambda_(n)`

Text Solution

Verified by Experts

The correct Answer is:
C
Since , `1/lambda =Rz^(2)(1/(1^(2))-1/(n^(2)))rArr ^^_(n)=1/(Rz^(2))+1/(Rz^(2))(1/(n^(2)))`
using binomial expansion
`^^_(n)=1/(Rz^(2))(1+1/(n^(2))),^^_(n)=1/(Rz^(2))+1/(Rz^(2))(1/(n^(2)))`
`^^_(n)=A+B/(lambda_(n)^(2))`
as`lambda_(n) = (2pir)/n = 2pi((n^(2)h^(2))/(4pi^(2)"mze"^(2)))1/n prop n `
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