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

  • question_answer
    Suppose potential energy between electron and proton at separation r is given by U= K In (r), where K is a constant. For such a hypothetical hydrogen atom, the ratio of energy difference between energy levels (n=1 and n=2) and (n     and n=4) is  

    A)        1

    B)  2    

    C)  3

    D)  4

    Correct Answer: A

    Solution :

    [a] \[-\frac{dU}{dr}=F\] (conservative force field) \[\Rightarrow F=\frac{-K}{r}\] provides the centrifugal force for circular motion of electron. \[\frac{m{{v}^{2}}}{r}=\frac{K}{r}\Rightarrow r=\frac{nh}{2\pi \sqrt{mK}}\] K.E. of electron \[=\frac{1}{2}m{{v}^{2}}=\frac{1}{2}K\] P.E. of electron = K In r E(n)=Total energy=K.E.+P.E.


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