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

  • question_answer
    In the Bohr model of a hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If \[{{a}_{0}}\] is the radius of the ground state orbit, m is he mass, e is the charge on the electron and \[{{\varepsilon }_{0}}\] is the vacuum permittivity, the speed of the electron is

    A)  0

    B) \[\frac{e}{\sqrt{{{\varepsilon }_{0}}a{{  }_{0}}m}}\]

    C) \[\frac{e}{\sqrt{4\pi {{\varepsilon }_{0}}a{{  }_{0}}m}}\]       

    D) \[\frac{\sqrt{4\pi {{\varepsilon }_{0}}a{{  }_{0}}m}}{e}\]

    Correct Answer: C

    Solution :

    [c] Centripetal force = Colombian force \[\frac{m{{v}^{2}}}{{{a}_{0}}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{e\times e}{a_{0}^{2}}\] \[\Rightarrow {{v}^{2}}=\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}.{{a}_{0}}.m}\Rightarrow v=\frac{e}{\sqrt{4\pi {{\varepsilon }_{0}}.{{a}_{0}}.m}}\]


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