A uniform magnetic field B exists in a region. An electron of charge q and mass m moving with velocity v enters the region in a direction perpendicular to the magnetic field. Considering Bohr angular

Question

A uniform magnetic field B exists in a region. An electron of charge q and mass m moving with velocity v enters the region in a direction perpendicular to the magnetic field. Considering Bohr angular momentum quantization, which of the following statement(s) is/are true?

TestHub · Accepted Answer

Hint: r = qB m v ​ m v r = 2 π nh ​ m v = 2 π r nh ​ r = 2 π r qB nh ​ ​ r 2 = 2 π qB nh ​ ⇒ r = 2 π qB nh ​ ​ r ∝ n ​ v = m qB r ​ = m qB ​ 2 π qB nh ​ ​ min v ​ = m 2 q 2 B 2 ​ × 2 π qB nh ​ ​ = 2 π m 2 n qBh ​ ​ = m 1 ​ qB ​ ℏ ​ E ​ = 2 1 ​ m v 2 = 2 1 ​ m [ 2 π m 2 n qB h ​ ] ​ E ∝ n ​ E 2 ​ − E 1 ​ = ( n 2 ​ − n 1 ​ ) 4 π m qBh ​ hf = ( n 2 ​ − n 1 ​ ) 4 π m qBh ​ n 2 ​ − n 1 ​ = 1 for successive levels ​

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