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Question

A proton, a direction ion and an α-particle of equal kinetic energy perform circular motion normal to a uniform magnetic field B. If the radii of their paths are rp,rd and rα respectively then [Here, qd=qp,md=2mp]

A
rα=rp>rd
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B
rα=rp<rd
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C
rα>rd>rp
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D
rα=rd=rp
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Solution

The correct option is C rα=rp<rd
Given, a proton q=+1m=mp a deutorium q=+1m=2mp a α particle q=+2m=4mp
hane equal Kinctic energy B= magnetic field.
We Know when a change particle enters in a magnetic field it perform circular motion with radius equal to.
r=mvqBr=2mKEqB
rproton =2×mp×KE1×Brdeutorium=2×2×mp×KE1×Brα=2×4×mp×KE2×B=2×mp×KE1×B
So, rproton =rα<rdeutorium (option B)

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