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Question:

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let λn, λg be the de Broglie wavelength of the electron in the nth state and the ground state respectively. 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). λ²n ≈ A + Bλ²n

λ²n ≈ λ

λn ≈ A + Bλ²n

λn ≈ A + Bλn

λ²n ≈ A + Bλ²n

Solution:

hc = En - Eg

hcAn = z⁴me⁴/4πε₀²ħ²[1/λ²n - 1/λ²g]

An = CONSTANT[1/λ²n - 1/λ²g]

An = Pλ²n + Q

so An = Qλ²nλ²n + 1

hence An = A + Bλ²n