A model for quantized motion of an electron in a uniform magnetic field B states that the flux passing through the orbit of the electron is n ( h / e ) where n is an integer, h is Planck's consta

Question

A model for quantized motion of an electron in a uniform magnetic field B states that the flux passing through the orbit of the electron is n ( h / e ) where n is an integer, h is Planck's constant and e is the magnitude of electron's charge. According to the model, the magnetic moment of an electron in its lowest energy state will be ( m is the mass of the electron)NEET 2025

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Magnetic moment ​ M = I A = I ( π r 2 ) M = ( 2 π r e u ​ ) ( π r 2 ) ​ Given B ( π r 2 ) = n ( e h ​ ) ⇒ r 2 = B π e h ​ … ( 2 ) ( ∵ n = 1 ) And when charge moving in external magnetic field then r = qB m u ​ r v ​ = m e B ​ … ( 3 ) ( ∵ q = e ) Put value from equation (2) and (3) in equation (1) ​ M = ( 2 π r e v ​ ) ( π r 2 ) M = 2 π e ​ ( m e B ​ ) π ( B π e h ​ ) M = 2 πm e h ​ ​

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