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)`
B. `(m_(p)/m_(e))^(2)`
C. `(m_(p)/m_(e))^(1//2)`
D. `(m_(p)/m_(e))^(3//2)`

Answer

C

Explanation

`S=1/2at^(2)=((eE)/m)t^(2)`
Now, `t^(2)/m` = Constant for same distance
Thus, `mpropt^(2)`
`therefore" "m_(e)/m_(p)=t_(e)^(2)/t_(p)^(2)" "thereforet_(p)/t_(e)=sqrt(m_(p)/m_(e))`
`i.e" "t_(2)/t_(1)=(m_(p)/m_(e))^(1//2)`