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# A proton and an alpha particle both enter a region of uniform magnetic field B, moving at right angles to the field B. If the radius of circular orbits for both the particles is equal and the kinetic energy acquired by proton is 1 MeV,  the energy acquired by the alpha particle will be

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a
1.5 MeV
b
1 MeV
c
4 MeV
d
0.5 MeV

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detailed solution

Correct option is B

The kinetic energy acquired by a charged particle in a uniform magnetic field B isK=q2B2R22m  as  R=mvqB=2mKqBwhere q and m are the charge and mass of the particle and R is the radius of circular orbit.∴ The kinetic energy acquired by proton is Kp=qp2B2Rp22mp and that by the alpha particle is Kα=qα2B2Rα22mα Thus, KαKp=qαqp2mpmαRαRp2 or Kα=Kpqαqp2mpmαRαRp2 Here, Kp=1MeV,qαqp=2,mpmα=14 and RαRp=1∴ Kα=(1MeV)(2)214(1)2=1MeV

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