If one were to apply the Bohr model to a particle of mass ' m ' and charge ' q ' moving in a plane under the influence of a magnetic field 'B', the energy of the charged particle in the n t h level will be:

Question

If one were to apply the Bohr model to a particle of mass ' m ' and charge ' q ' moving in a plane under the influence of a magnetic field 'B', the energy of the charged particle in the n t h level will be:, n h q B π m, n h q B 4 π m, n h q B 2 π m, n h q B 8 π m

MARKS App · Accepted Answer

For a charge q moving in a uniform magnetic field B f m = m v 2 R q V B = m v 2 R ⇒ m v 2 = q V B R ⇒ 1 2 m v 2 = q V B R 2 ⇒ E n e r g y = q V B R 2 ( 1 ) By Bohr's quantization condition, Angular momentum L = n h 2 π ⇒ m v R = n h 2 π ⇒ v R = n h 2 π m ( 2 ) Put ( 2 ) in ( 1 ) ⇒ E n e r g y = q B 2 n h 2 π m = q B n h 4 π m

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