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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2012

  • question_answer
    An electron accelerated through a potential difference of V volts has a wavelength\[\lambda \] associated with it. Mass of proton is nearly 2000 times that of an electron. In order to have the same wavelength\[\lambda \]for the proton, it must be accelerated through a potential difference of

    A)  2000 V volt   

    B)  20 V volt

    C)  V/2000 volt   

    D)  \[\sqrt{2000}\]V volt

    Correct Answer: C

    Solution :

     Energy of an accelerated particle is given as \[{{E}_{n}}=qV\] and wavelength, \[\lambda =\frac{h}{p}=\frac{h}{\sqrt{2mE}}=\frac{h}{\sqrt{2mqV}}\] Here,    \[{{m}_{e}}{{V}_{e}}={{m}_{p}}{{V}_{p}}\] Or \[{{V}_{p}}=\frac{{{m}_{e}}{{V}_{e}}}{{{m}_{p}}}=V\times \frac{1}{2000}\] \[=\frac{V}{2000}volt\]


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