An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let λ n , λ g be the de Broglie wavelength of the electron in the n t h state and the ground state

Question

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

TestHub · Accepted Answer

2 π r = n ⋋ n ⋋ n = 2 π r n ∴ r = r o n 2 ⋋ n = 2 π n r o n 2 = n 2 π r o … . . i 1 ∧​ n = R 1 1 2 - 1 n 2 ∧​ n = 1 R 1 + 1 n 2 - 1 ∧​ n = 1 R 1 + 1 n 2 … … … . . ii from ( i ) and ( ii ) ∧​ n = 1 R 1 + 4 n 2 r o 2 ⋋ n 2 = A + B ⋋ n 2

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