JEE Main & Advanced Physics Photo Electric Effect, X- Rays & Matter Waves Question Bank Critical Thinking

  • question_answer
    A photon and an electron have equal energy E. \[{{\lambda }_{\text{photon}}}/{{\lambda }_{\text{electron}}}\] is proportional to [UPSEAT 2003; IIT-JEE (Screening) 2004]

    A)            \[\sqrt{E}\]                           

    B)            \[1/\sqrt{E}\]

    C)            \[1/E\]                                    

    D)            Does not depend upon E

    Correct Answer: B

    Solution :

                       \[{{\lambda }_{photon}}=\frac{hc}{E}\]  and \[{{\lambda }_{proton}}=\frac{h}{\sqrt{2\,mE}}\]                    Þ \[\frac{{{\lambda }_{photon}}}{{{\lambda }_{electron}}}=c\sqrt{\frac{2m}{E}}\]Þ \[\frac{{{\lambda }_{photon}}}{{{\lambda }_{electron}}}\propto \frac{1}{\sqrt{E}}\]


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