Question

An electron of mass $m_{e}$ initially at rest moves through a certain distance in a uniform electric field in time $t_{1}$. A proton of mass $m_{p}$ 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

• A. 1
• B. $(m_{p}/m_{e})^{1/2}$
• C. $(m_{e}/m_{p})^{1/2}$
• D. 1836

Answer 1

Answer: (B)

$(m_{p}/m_{e})^{1/2}$

Answer 2

For electron $s = \frac{eE}{m_{e}} \times t_{1}^{2}$,

For proton $s = \frac{eE}{m_{p}} \times t_{2}^{2}$

∴ $\frac{t_{2}^{2}}{t_{1}^{2}} = \frac{m_{p}}{m_{e}} \Rightarrow \frac{t_{2}}{t_{1}} = \sqrt{\frac{m_{p}}{m_{e}}} = \left( \frac{m_{p}}{m_{e}} \right)^{1/2}$