JEE Mains · Physics · STD 12 - 12. atoms
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
- A \(n\left( {\frac{{hqB}}{{2\pi m}}} \right)\)
- B \(n\left( {\frac{{hqB}}{{8\pi m}}} \right)\)
- C \(n\left( {\frac{{hqB}}{{4\pi m}}} \right)\)
- D \(n\left( {\frac{{hqB}}{{\pi m}}} \right)\)
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.…
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