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

Options

A. 1
B. `(m_(p)//m_(e))^(1//2)`
C. `(m_(e)//m_(p))^(1//2)`
D. 1836

Answer

B

Explanation

Acceleration in uniform electric field is given by
`a = (F)/(m) = (qE)/(m)`
Given that,
`X_(e) = X_(p)`
`(1)/(2) a_(e) t_(1)^(2) = (1)/(2) a_(p) t_(2)^(2)`
`(t_(2))/(t_(1)) = sqrt((a_(e))/(a_(p))) = sqrt((eE//m_(e))/(eE//m_(p))) = sqrt((m_(p))/(m_(e)))`