If one were to apply 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 \(n^{th}\) level will be

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Answer & Solution

Correct Answer

(C) \(n\left( {\frac{{hqB}}{{4\pi m}}} \right)\)

Step-by-step Solution

Detailed explanation

\(q V B=\frac{m v^{2}}{r}\) ..... \((i)\)

\(\frac{n h}{2 \pi}=m v r\) ..... \((ii)\)

Multiplying equation \((i)\) and \((ii)\),

\(\frac{q B n h}{2 \pi}=m^{2} v^{2}\)

Now multiplying both sides by \(\frac{1}{2 m}\)

\(n \frac{q B h}{4 \pi m}=\frac{1}{2} m v^{2}\)

i.e. \(\quad \mathrm{KE}=n\left[\frac{q B h}{4 \pi m}\right]\)

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