A proton and helium nucleus are shot into a magnetic field at right angles to the field with same kinetic energy. Then the ratio of their radii is

Options

A. `1 : 1`
B. `1 : 2`
C. `2 : 1`
D. `1 : 4`

Answer

A

Explanation

Kinetic energy of a charged particle,
`K = (1)/(2) mv^(2) or v= sqrt((2K)/(m))`
Radius of the circular path of a charged particle in a uniform magnetic field is
`r= (mv)/(q B) = (m)/(qB) sqrt((2K)/(m)) = (sqrt(2Km))/(qB)`
Since K and B are same for both the particles,
`:. r prop (sqrtm)/(q)`
`:. (r_(p))/(r_(prop)) = sqrt((m_(p))/(m_(q))) xx (q_(alpha))/(q_(p))` (`:' alpha` is a helium nucleus)
`= sqrt((m)/(4m)) xx (2e)/(e ) = 1`
`r_(p) : r_(alpha) =1 : 1`