BHU PMT BHU PMT (Mains) Solved Paper-2005

  • question_answer
    Out of a photon and an electron the equation E = pc, is valid for:

    A)  both                                    

    B)  neither

    C)  photon only                     

    D)  electron only

    Correct Answer: C

    Solution :

                     Relativistic energy is given by \[E=\frac{{{m}_{0}}{{c}^{2}}}{\sqrt{1-{{v}^{2}}/{{c}^{2}}}}\] Or           \[{{E}^{2}}=\frac{{{m}_{0}}{{c}^{6}}}{\sqrt{{{c}^{2}}-{{v}^{2}}}}\]                               ?? (i) Momentum is given by                 \[p=\frac{{{m}_{0}}v}{\sqrt{1-{{v}^{2}}/{{c}^{2}}}}\] Or           \[{{p}^{2}}{{c}^{2}}=\frac{m_{0}^{2}{{c}^{4}}{{v}^{2}}}{{{c}^{2}}-{{v}^{2}}}\]                              ...(ii) \[\therefore \]  \[{{E}^{2}}-{{p}^{2}}{{c}^{2}}=m_{0}^{2}{{c}^{4}}\] or          \[{{E}^{2}}={{p}^{2}}{{c}^{2}}+m_{0}^{2}{{c}^{4}}\] For photon, rest mass\[{{m}_{0}}=0,\]so\[E=pc\] For electron,\[{{m}_{0}}\ne 0,\]so\[E\ne pc\]


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