An `alpha` - particle and a proton moving with the same kinetic energy enter a region of uniform magnetic field at right angles to the field . The ratio of the radii of the paths of `alpha`- particle to that of the proton is

Options

A. `1 : 1`
B. `1 : 2`
C. `1: 4`
D. `1 : 8`

Answer

A

Explanation

Radius of the circular path of a charged particle in the magnetic field is `r = (mv)/(qB)`
Kinetic energy of the charged particle , `K = (1)/(2) mv^(2)` or `v = sqrt((2K)/(m))`
`therefore r = (m)/(qB) sqrt((2K)/(m)) = (sqrt(2mK))/(qB)`
`r prop (sqrtm)/(q)` For the same value of K and B .
`therefore (r_(alpha))/(r_(p)) = sqrt((m_(alpha))/(m_(p))) xx (q_(p))/(q_(alpha)) = sqrt((4m)/(m)) xx (e)/(2e) = 1`