• # 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) $3\frac{{{m}_{0}}{{v}_{0}}}{{{q}_{0}}{{E}_{0}}}$

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