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Question

Four charge particles α, proton, deuteron and Li+++ are projected in a uniform magnetic field perpendicular to their velocity. Consider the radius of the particle having least radius out of these to be r, List-1 gives the particles and List-2 gives value of n, where nr is the radius of the particle.
Match the entries correctly in the lists if kinetic energy of each particle is same.
List-1List-2(I)α(P)1(II)Proton(Q)2(III)Deuteron(R)3(IV)Li+++(S)37(T)327(U)32

A
IS, IIS, IIIT, IVP
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B
IP, IIP, IIIT, IVQ
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C
IP, IIP, IIIQ, IVS
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D
IS, IIS, IIIP, IVP
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Solution

The correct option is A IS, IIS, IIIT, IVP
R=mvqB=2mEqB

Rα=2× 4mE2eB=2mEeB=R0

Rp=2mEeB=R0

Rd=2×2mEeB=22mEeB=2R0

RLi=2×7mE3eB=732mEeB=73R0

Let, Least radius =73R0=rR0=3r7
Hence, Rα=R0=3r7
Rp=R0=3r7
Rd=2R0=327r
RLi=73R0=r

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