RAJASTHAN PMT Rajasthan - PMT Solved Paper-2010

  • question_answer
    An electron is accelerated through a potential difference of 1000 V. Its velocity is nearly

    A)  \[3.8\,\times {{10}^{7}}m/s\]    

    B)  \[\text{1}\text{.9 }\!\!\times\!\!\text{ 1}{{\text{0}}^{6}}\text{m/s}\]

    C)  \[\text{1}\text{.9 }\!\!\times\!\!\text{ 1}{{\text{0}}^{7}}\text{m/s}\]     

    D)         \[\text{5}\text{.7 }\!\!\times\!\!\text{ 1}{{\text{0}}^{7}}\text{m/s}\]

    Correct Answer: C

    Solution :

    If the voltage given is\[V\], then the energy of electron                 \[=\frac{1}{2}m{{v}^{2}}=eV\]                 \[v=\sqrt{\frac{2eV}{m}}\]                    \[=\sqrt{\frac{2\times 1.6\times {{10}^{-19}}\times 1000}{9.1\times {{10}^{-31}}}}\]                   \[=1.875\times {{10}^{7}}\]                   \[=1.9\times {{10}^{7}}\,\,m/s\]


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