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Question:

A proton, an electron, and a Helium nucleus have the same energy. They are in circular orbits in a plane due to a magnetic field perpendicular to the plane. Let rp, re, and rHe be their respective radii. Then,

re > rp > rHe

re < rp = rHe

re < rp < rHe

re > rp = rHe

Solution:

Correct option is C. re < rp < rHe
r = mv/qB = 2mK/qB
For same energy K, r is proportional to m/q.
rHe/rp = (mHe/mp) * (qp/qHe) = (4/1)(1/2) = 2
rHe = 2rp
re/rp = (me/mp) * (qp/qe) = (1/1836)
(1/1) ≈ 0.0005
re << rp
Therefore, re < rp < rHe