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

Answer

A

Explanation

Force acting on a charged particle in a uniform electric field is given by F = qE
The acceleration imparted to the particle is `a = (qE)/(m)`
Distance travelled by the particle in time t is
`d = (1)/(2) a t^(2) = (1)/(2)((qE)/(m))t^(2) " "(because u = 0)`
For the given problem, we have `d_(p) = d_(e)`
`:. (t_(p)^(2))/(m_(p)) = (t_(e)^(2))/(m_(e))` or `(t_(p))/(t_(e)) = ((m_(p))/(m_(e)))^(1//2)` or `(t_(2))/(t_(1)) = ((m_(p))/(m_(e)))^(1//2) (because q_(e) = q_(p))`