Question

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 the same uniform electric field. Neglecting the effect of gravity, the ratio of $t_1$ to $t_2$ is _______.

• 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 ${\left(m_p/m_e\right)}^{1/2}$

Electric force = inertial force

$qE=ma$

$a=\frac{qE}{m},hence,accelerationa\propto \frac{1}{m}\dots \dots \left(1\right)$

Apply equation of kinematic

$s=ut+\frac{1}{2}a{t}^2(initalvelocity=0)$

$s=\frac{1}{2}a{t}^2,hence,forequal\text{distance}(t\propto \sqrt{\frac{1}{a}})\dots \dots \left(2\right)$

From (1) and (2)

$\frac{t_p}{t_e}=\sqrt{\frac{a_e}{a_p}}=\sqrt{\frac{m_p}{m_e}}={\left(\frac{m_p}{m_e}\right)}^{1/2}$

Hence, ratio of time duration for proton and electron is ${\left(\frac{m_p}{m_e}\right)}^{1/2}$