An `(alpha)`-particle and a proton are both simultaneously projected in opposite direction into a region of constant magnetic field perpendicular to the direction of the field. After some time it is found that the velocity of the `(alpha)`-particle has changed in a direction by `45^(@)`. Then at this time, the angle between velocity vectors of `(alpha)`-particle and proton is

Options

A. `90^(@)`
B. `45^(@)`
C. `45^(@)+90^(@)`
D. `(45^(@)+90^(@))/2`

Answer

c

Explanation

`omega_(alpha) ((2e)B)/(4m) =1/2 (eB)/m`
`omega_(p)=(eB)/m`
`theta_(alpha)=45^(@)`
`theta_(p)=90^(@)` from their original directions.