An electron of mass $n_{e}$ initially at rest moves through a certain distance in a uniform electric field in time $t_1$ . A proton of mass $n_p$ also initially at rest takes time $t_2$ to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio of $t_2 / t_1$ is nearly equal to
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For electron $s = \frac{eE}{m_e} \times t_1^2$ , For proton $s = \frac{eE}{m_p} \times t_2^2$
∴ ∴ $\frac{t_2^2}{t_1^2} = \frac{m_p}{m_e} \Rightarrow \frac{t_2}{t_1} = \sqrt{\frac{m_p}{m_e}} = \left(\frac{m_p}{m_e}\right)^{1/2}$
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