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 $\frac{t_2}{t_1}$ is nearly equal to,

• A. 1
• B. ${\left(\frac{m_p}{m_e}\right)}^{\frac{1}{2}}$
• C. ${\left(\frac{m_e}{m_p}\right)}^{\frac{1}{2}}$
• D. 1836

Answer 1

The correct option is B ${\left(\frac{m_p}{m_e}\right)}^{\frac{1}{2}}$

$F=qE.S=\frac{1}{2}a{t}^2\Rightarrow S=\frac{1}{2}\left(\frac{qE}{me}\right)t^2$
$S_e=\frac{1}{2}\left(\frac{qE}{me}\right)t^2$ and $S_p=\frac{1}{2}\left(\frac{qE}{m_p}\right)t^2$
$S_e=S_p\Rightarrow \frac{t_1^2}{me}=\frac{t_2^2}{m_p}$
$\Rightarrow \frac{t_2}{t_1}={\left(\frac{m_p}{m_e}\right)}^{\frac{1}{2}}$