A proton and a deuteron with the same initial kinetic energy enter a magnetic field in a direction perpendicular to the direction of the field.The ratio of the radii of the circular trajectories described by them is

Options

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

Answer

B

Explanation

Momentum (mv) = `sqrt(2mE)` where E = Kinetic Energy.
`therefore` `("Momentum of proton")/("Momentum of deuteron)"` = `sqrt(m_(p)/(m_(d))` ...(i)
For circular motion of a particle, `Bev = (mv^(2))/(R)` or` R = (mv)/(Be) = ("momentum")/(Be)` ....(ii)
From (i) and (ii), we get `therefore(R_(p))/(R_(d)) = sqrt(m_(p)/(m_(d)) = sqrt(1)/(2)` or `(R_(p))/(R_(d)) = (1)/(sqrt2)`