An `alpha` particle and a proton having same momentum enter into a region of uniform magnetic field and move in circular paths. The ratio of the radii of curvature of their paths, `(R_(alpha))/(R_(p)` in the field is

Options

A. `(1)/(2)`
B. `(1)/(4)`
C. 1
D. 4

Answer

A

Explanation

`alpha-"particles"=_(2)He^(4):."charge"=2e`
`"particles"=_(1)H^(1):."charge"=e`
Momentum, `m_(alpha)v_(alpha)=m_(p)v_(p)`
For circular motion in uniform magnetic field,
`Bqv=(mv^(2))/(R)orBqR=mv" ":.Bq_(alpha)R_(alpha)=Bq_(p)R_(p)`
or `(R_(alpha))/(R_(p))(q_(p))/(q_(alpha))=(e)/(2e)=(1)/(2):.(R_(alpha))/(R_(p))=(1)/(2)`