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Question:

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii re, rp, rα respectively in a uniform magnetic field B. The relation between re, rp, rα is?

re<rα<rp

re>rp=rα

re<rp<rα

re<rp=rα

Solution:

For circular orbit in magnetic field
Radius = r = mv/qB
mv = √(2mK) (K=kinetic energy)
r = √(2mK)/qB
In the question it is given that K (kinetic energy) is same for all the particles
re = √(2meK)/eB
rp = √(2mpK)/eB
rα = √(2(4mp)K)/2eB
Hence re < rp = rα