A proton, at deuteron and an `alpha`-particle are projected perpendicular to the direction of a uniform magnetic field with same kinetic energy. The ratio of the radii of the circular paths described by them is

Options

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

Answer

A

Explanation

According to the question, magnetic uniform and the kinetic energy for each particle are same. We know that,
`r=(mv)/(qB)=(sqrt(2m(K.E)))/(qB)`
`r alpha (m)/(q)`
`r_(p): r_(d): r_(alpha)= sqrt((m)/(q)): sqrt((2m)/(q)):sqrt((m)/(q))`
`= 1: sqrt(2):1`