A proton (charge +*e*, mass *m _{p}*), a deuteron (charge +

*e*, mass 2

*m*), and an alpha particle (charge +2

_{p}*e*, mass 4

*m*) are accelerated from rest through a common potential difference Δ

_{p}*V*. Each of the particles enters a uniform magnetic field , with its velocity in a direction perpendicular to . The proton moves in a circular path of radius

*r*.

_{p}
(a) In terms of *r _{p}*, determine the radius

*r*of the circular orbit for the deuteron.

_{d}
*r _{d}* =

(b) In terms of

*r*, determine the radius

_{p}*r*

_{}for the alpha particle.

*r*

_{}=