JEE Main & Advanced JEE Main Paper Phase-I (Held on 07-1-2020 Evening)

  • question_answer
    An electron (of mass m) and a photon have the same energy E in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is (c = speed of light in vacuum)                                                                 [JEE MAIN Held on 07-01-2020 Evening]

    A) \[\frac{1}{c}{{\left( \frac{E}{2m} \right)}^{\frac{1}{2}}}\]

    B) \[{{\left( \frac{E}{2m} \right)}^{\frac{1}{2}}}\]

    C) \[c\,{{(2mE)}^{\frac{1}{2}}}\]      

    D) \[\frac{1}{c}{{\left( \frac{2E}{m} \right)}^{\frac{1}{2}}}\]

    Correct Answer: A

    Solution :

    [a] \[{{\lambda }_{e}}=\frac{h}{{{p}_{e}}}=\frac{h}{\sqrt{2\,mE}}\] \[\frac{hc}{{{\lambda }_{P}}}=E\Rightarrow {{\lambda }_{p}}=\frac{hc}{E}\] \[\Rightarrow \,\frac{{{\lambda }_{e}}}{{{\lambda }_{p}}}=\frac{1}{\sqrt{2mE}}\frac{E}{c}=\sqrt{\frac{E}{2m}}\cdot \frac{1}{c}\]

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