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JEE Main & Advanced Physics Atomic Physics Question Bank Self Evaluation Test - Atoms

  • question_answer
    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 nth 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) \[n\left( \frac{hqB}{\pi m} \right)\]

    Correct Answer: C

    Solution :

    [c] \[qVB=\frac{m{{v}^{2}}}{r}\] and \[\frac{nh}{2\pi }=mvr\] Multiplying equation (i) and (ii), \[\frac{qBnh}{2\pi }={{m}^{2}}{{v}^{2}}\] Now multiplying both sides by\[\frac{1}{2m}\], \[n\frac{qBh}{4\pi m}=\frac{1}{2}m{{v}^{2}}\text{ i}\text{.e}\text{. }KE=n\left[ \frac{qBh}{4\pi m} \right]\]


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