KVPY Sample Paper KVPY Stream-SX Model Paper-29

  • question_answer
    A charge particle \[{{q}_{0}}\]of mass \[{{m}_{0}}\] is projected along the y-axis at t = 0 from origin with a velocity\[{{V}_{0}}\]. If a uniform electric field \[{{E}_{0}}\] also exists along the x-axis, then the time at which debroglie wavelength of the particle becomes half of the initial value is:

    A) \[\frac{{{m}_{0}}{{v}_{0}}}{{{q}_{0}}{{E}_{0}}}\]

    B) \[2\frac{{{m}_{0}}{{v}_{0}}}{{{q}_{0}}{{E}_{0}}}\]

    C) \[\sqrt{3}\frac{{{m}_{0}}{{v}_{0}}}{{{q}_{0}}{{E}_{0}}}\]

    D) \[3\frac{{{m}_{0}}{{v}_{0}}}{{{q}_{0}}{{E}_{0}}}\]

    Correct Answer: C

    Solution :

    \[{{v}_{i}}={{v}_{0}}\]          and      \[{{v}_{f}}=\sqrt{v_{0}^{2}+{{\left( \frac{qE}{m}t \right)}^{2}}}\]and             \[{{v}_{f}}=2{{v}_{i}}\,\,\,\,\Rightarrow \,\,\,\,t=\sqrt{3}\,\frac{{{m}_{0}}{{v}_{0}}}{{{q}_{0}}{{E}_{0}}}\]

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