Doubly ionised helium atoms and hydrogen ions are final velocities of helium and of the hydrogen ions is :

Options

A. 2
B. `sqrt2`
C. `(1)/(2)`
D. `(1)/(sqrt2)`

Answer

D

Explanation

`((1)/(2)Me_(he)v_(he)^(2))/((1)/(2)M_(h)v_(h)^(2))=(qV)/(q.V)=(q)/(q.)" "....(1)`
Here q= charge on helium ion
`:.` q= change on hydrogen ion
`:. (q)/(q.)=(2)/(1) and (M_(h))/(M_(he))=(1)/(4)`
From eqn. `(1),((v_(he))^(2))/((v_(h))^(2))=(q)/(q)xx(M_(h))/(M_(he))`
From eqn . `=(2)/(1)xx(1)/(4)=(1)/(2)`
`:. (v_(he))/(v_(h))=(1)/(sqrt(2))`