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Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively rₚ, r_d and r_α. Which one of the following relation is correct?

1. (a) r_α = rₚ = r_d
2. (b) r_α = rₚ < r_d
3. (c) r_α < r_d > rₚ
4. (d) r_α > r_d > rₚ

Correct answer: (b) r_α = rₚ < r_d

Solution

For equal KE, r = sqrt(2mE)/(qB) ~ sqrt(m)/q. Proton: sqrt(1)/1=1; deuteron: sqrt(2)/1=1.41; alpha: sqrt(4)/2=1. Hence r_alpha = r_p < r_d (option b).

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