The ratio of momenta of an electron and an alpha particle which are accelerated from rest through a potential difference of 100 volts is :

Options

A. 1
B. `sqrt((2m_(e))/(m_(alpha)))`
C. `sqrt((m_(e))/(m_(alpha)))`
D. `sqrt((m_(e))/(2m_(alpha)))`

Answer

D

Explanation

Energy of particle is
`U=(P^(2))/(2m)` (p is momentum)
`:.(p_(e)^(2))/(2m_(e))=q_(e)V" "....(1)`
` and (p_(alpha)^(2))/(2m_(alpha))=q_(alpha)V " "....(2)`
Dividing we get
`((P_(e))/(P_(alpha)))^(2)((m_(alpha))/(m_(e)))=(q_(e))/(q_(alpha))`
`:.(p_(e))/(p_(alpha))= sqrt((q_(e))/(q_(alpha))*(m_(e))/(m_(alpha)))`
`:. (q_(e))/(p_(alpha))=(1)/(2)`
`:. (P_(e))/(P_(alpha))= sqrt((m_(e))/(2m_(alpha)))`