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MHT CET · Physics · Atomic Physics

Bohr model is applied to a particle of mass \(m\) and charge \(q\) is moving in a plane under the influence of a transverse magnetic field (B). The energy of the charged particle in the second level will be
\(\text { ( } \mathrm{h}=\text { Planck's constant } \text { ) }\)

  1. A \(\frac{\mathrm{qBh}}{\pi \mathrm{m}}\)
  2. B \(\frac{\mathrm{q}^2 \mathrm{~B}^2 \mathrm{~h}^2}{4 \pi \mathrm{~m}}\)
  3. C \(\frac{\mathrm{qBh}}{2 \pi \mathrm{~m}}\)
  4. D \(\frac{2 \mathrm{qBh}}{\pi \mathrm{m}}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{\mathrm{qBh}}{2 \pi \mathrm{~m}}\)

Step-by-step Solution

Detailed explanation

\(qvB = \frac{mv^2}{r}\) and \(mvr = n\frac{h}{2\pi} \implies v^2 = \frac{nhqB}{2\pi m^2}\) \(E = \frac{1}{2}mv^2 = \frac{1}{2}m\left(\frac{nhqB}{2\pi m^2}\right) = \frac{nhqB}{4\pi m}\)