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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 r_he be their respective radii. Then:

1. rₑ < rₚ < r_he
2. rₑ > rₚ = r_he
3. rₑ < rₚ = r_he
4. rₑ > rₚ > r_he

Correct answer: rₑ < rₚ = r_he

Solution

For equal energy, r = sqrt(2mE)/(qB) so r is proportional to sqrt(m)/q. For He: sqrt(4m_p)/2 = sqrt(m_p)/1 = same as proton, so r_p = r_he. The electron's tiny mass makes r_e the smallest, giving r_e < r_p = r_he.

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