A proton, a deuteron and an `alpha`-particle with the same KE enter a region of uniform magnetic field, moving at right angles to B. What is the ratio of the radii of their circular paths ?

Options

A. `1:sqrt(2) : sqrt(2)`
B. `1:1:sqrt(2)`
C. `sqrt(2):1:1`
D. `1:sqrt(2):1`

Explanation

For circular path in magnetic field.
`r =sqrt(2mE)/(qB)`, E = kinetic energy
So,
`r_(1):r_(2):r_(3) = sqrt(m_(1)/q_(1)) : sqrt(m_(2)/q_(2)) : sqrt(m_(3)/q_(3)) = sqrt(1)/e : sqrt(2)/e : sqrt(4)/(2e) = 1: sqrt(2) : 1`