Question

An `alpha` - particle and a proton are accelerated through same potential difference. Find the ratio `(v_(a)//v_(p))` of velocities acquired by two particles.

Answer 1

Gain in KE of particle = Qv
`(1)/(2)"m"_(p)"v"_(p)^(2) = K_(p) = q_(p)V_(p) .............(i)V_(p) = Vprop = V`
`(1)/(2)"m"_(prop)"v"_(prop)^(2) = K_(prop) = q_(prop)V_(prop) .............(i)`
(ii)/(i)
`(m_(prop)v_(prop)^(2))/(m_(p)v_(p)^(2)) = (q_(prop))/(q_(p)) = (2)/(1)`
`(v_(prop)^(z))/(v_(p)^(2)) = (m_(p) xx 2)/(m_(alpha) xx 1) = (Zm_(p))/(4m_(p) xx 1) = (1)/(2)`
`V_(prop) : V_(p) = 1 : sqrt(2)`