A proton and an `alpha`-particle start from rest in a uniform electric field. The ratio of times taken by them to travel the same distance in the field is

Options

A. `sqrt5:sqrt2
B. `sqrt3:1`
C. `2:1`
D. `1:sqrt2`

Answer

D

Explanation

Acceleration of `alpha`-particle, `a_(r)=(qE)/m=(2eE)/4`
Acceleration of photon,
`a_(p)=(eE)/1`
They travel same distances in time `t_(1)andt_(2)`.
`rArr1/2((2eE)/4)t_(1)^(2)=1/2((eE)/1)t_(2)^(2)rArrt_(2)^(2)/t_(1)^(2)=1/2rArrt_(2)/t_(1)=1/sqrt2`