Question

An electron of mass $m_e$, initially at rest, move 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 $t_2/t_1$ is nearly equal to

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

Answer 1

The correct option is B ${\left(m_p{/m}_e\right)}^{1/2}$

$s=\frac{1}{2}a{t}^2=\frac{1}{2}\frac{F}{m}{t}^2$

$t\alpha \sqrt{m}$

$\frac{t_1}{t_2}=(\frac{m_e}{m_p}{)}^{1/2}$

$\frac{t_2}{t_1}=(\frac{m_p}{m_e}{)}^{1/2}$