A Bohr hydrogen atom undergoes a transition n = 5 → n = 4 and emits a photon of frequency υ . Frequency of circular motion of electron in n = 4 orbit is v 4 . The ratio ν ν 4 is

Question

A Bohr hydrogen atom undergoes a transition n = 5 → n = 4 and emits a photon of frequency υ . Frequency of circular motion of electron in n = 4 orbit is v 4 . The ratio ν ν 4 is, 18 25, 16 25, 9 25, 8 25

MARKS App · Accepted Answer

E n = - m z 2 e 4 8 ε 0 2 n 2 h 2 So, h v = + m z 2 e 4 8 ε 0 2 h 2 1 16 - 1 25 ∴ v = m z 2 e 4 8 ε 0 2 h 3 9 16 × 25 . . . ( 1 ) And frequency v 4 = 1 T = v 2 π r = Z e 2 2 ε 0 n h 1 2 π π m z e 2 ε 0 h 2 n 2 = z 2 e 4 m 4 ε 0 2 n 3 h 3 . . . ( 2 ) ∴ v v 4 = 18 25 = 0.72

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