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An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii rₑ, rₚ and r_α respectively in a uniform magnetic field B. The relation between rₑ, rₚ, r_α is

1. rₑ < rₚ = r_α
2. rₑ < rₚ < r_α
3. rₑ < r_α < rₚ
4. rₑ = r_α < rₚ

Correct answer: rₑ < rₚ = r_α

Solution

The radius of the circular orbit in a magnetic field is directly proportional to the momentum of the particle and inversely proportional to its charge. Since the electron has a much smaller mass and charge compared to the proton and alpha particle, it will have a smaller radius for the same kinetic energy, leading to the relation rₑ < rₚ = r_α, as both the proton and alpha particle have the same charge-to-mass ratio.

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