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JCECE Engineering JCECE Engineering Solved Paper-2015

  • question_answer
    A stationary hydrogen atom emits photon corresponding to the first line of Lyman series. If \[R\] is the Rydberg's constant and m is the mass of the atom, then the velocity acquired by the atom is (neglect energy absorbed by the photon)

    A) \[\frac{4m}{Rh}\]                                            

    B) \[\frac{Rh}{4m}\]

    C) \[\frac{3Rh}{4m}\]                                         

    D) \[\frac{4m}{3Rh}\]

    Correct Answer: C

    Solution :

    For first line of Lyman series,                 \[\frac{1}{\lambda }=R\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{2}^{2}}} \right)=R\left( 1-\frac{1}{4} \right)=\frac{3}{4}R\] Again we have momentum,                 \[p=mv\]or\[\frac{h}{\lambda }=mv\]\[\text{or}\]\[v=\frac{h}{m\lambda }\] Putting the value of\[\lambda \], we have                 \[v=\frac{h}{m}\left( \frac{3}{4}R \right)=\frac{3hR}{4m}\]


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