Starting from the rest, an electron of mass `m_(e)` and a proton of mass `m_(p)` travel through a certain distance in a uniform electric field in times `t_(1)` and `t_(2)`, respectively. Find out the ratio `t_(2)//t_(1)`, neglecting the influence of gravity.

Explanation

In a uniform electric field of intensity E, the force acting on a charge q is F=qE and its acceleration, `a=(qE)/m`
The distance travelled from rest in time t,
`s=1/2at^(2)=1/2((qE)/m)t^(2)`
For electron, `s_(e)=1/2((qE)/(m_(e)))t_(1)^(2),` for proton, `s_(p)=1/2((qE)/(m_(p)))t_(2)^(2)`
Given, `s_(e)=s_(p),` so we have,
`1/2((qE)/(m_(e)))t_(1)^(2)=1/2((qE)/(m_(p)))t_(2)^(2)` or, `1/(m_(e))t_(1)^(2))=1/(m_(p))t_(2)^(2)`
or, `(t_(2)^(2))/(t_(1)^(2))=(m_(p))/(m_(e))` or, `(t_(2))/(t_(1))=sqrt((m_(p))/(m_(e)))`