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Question

An electron from various states of hydrogen atom emit radiation to come to the ground state. Let λn,λg be the de Broglie wavelength of the ground state repectively. Let Λn be the wavelength of the emitted photon in the transition from the nth state to the ground state. For large n, (A, B are constants)

A
Λ2nA+Bλ2n
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B
Λ2nλ
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C
ΛnA+Bλ2n
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D
ΛnA+Bλn
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Solution

The correct option is C ΛnA+Bλ2n
The wavelength of emitted photon from nth state of the ground state,
1λn=R.Z2(1121n2)
λn=1RZ2(11n2)1
Since, n is very large, using the binomial theorem,
Λn=1RZ2(1+1n2)
Λn=1RZ2+1RZ2(1n2)
As we know, λn=2nrn=2π(n2h24π2mZe2)1nαn
λnA+Bλ2n

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