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VIT Engineering VIT Engineering Solved Paper-2010

  • 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 the mass and \[e\] is 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 :

    Centripetal force == force of attraction of nucleus on electron \[\frac{m{{v}^{2}}}{{{a}_{0}}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{{{e}^{2}}}{a_{0}^{2}}\] \[v=\frac{e}{\sqrt{4\pi {{\varepsilon }_{0}}m{{a}_{0}}}}\]


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