JEE Main & Advanced Physics Photo Electric Effect, X- Rays & Matter Waves Question Bank Self Evaluation Test - Dual Nature of Radiation and Matter

  • question_answer
    A proton has kinetic energy E = 100 keV which is equal to that of a photon. The wavelength of photon is \[{{\lambda }_{2}}\] and that of proton is \[{{\lambda }_{1}}.\] The ration of \[{{\lambda }_{2}}/{{\lambda }_{1}}\] is proportional to

    A) \[{{E}^{2}}\]

    B) \[{{E}^{1/2}}\]

    C) \[{{E}^{-1}}\] 

    D) \[{{E}^{-1/2}}\]

    Correct Answer: D

    Solution :

    [d] For photon, \[{{\lambda }_{2}}=\frac{hc}{E}\]                                            ?.(i) For proton, \[p=\sqrt{2mE}\] \[{{\lambda }_{1}}=\frac{h}{p}=\frac{h}{\sqrt{2mE}}\]                        ?(ii) \[\frac{{{\lambda }_{2}}}{{{\lambda }_{1}}}=\frac{hc}{E\times \frac{h}{\sqrt{2mE}}}\propto {{E}^{-1/2}}\]


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