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Question

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.

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Solution

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=0.5mv2
v2=4v2
vv=4=2

radius of charged particle in uniform magnetic field is r=mvqB

rr=mm×vv×qq=14×21×2qq=11

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