A proton and an alpha particle having the same kinetic energy are allowed to pass through a uniform magnetic field perpendicular to the direction of their motion. Compare the radii of the paths of proton and alpha particle.
a proton has a mass= m & charge = q
mass of an alpha particlem' = 4m & charge q' = 2q
K.e of proton = K.e of alpha particle
0.5mv2=0.5m′v′2
v2=4v′2
vv′=√4=2
radius of charged particle in uniform magnetic field is r=mvqB
rr′=mm′×vv′×q′q=14×21×2qq=11