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

Engineering

Physics

Motion of Charged Particle in Uniform Magnetic Field

Question

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

r_α > r_d > r_p

r_α = r_p = r_d

r_α = r_d > r_p

r_α = r_p < r_d

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

$R = \frac{mv}{qB} = \frac{\sqrt{2 mk}}{qB}$

$R_{p} : R_{d} : R_{α} = \frac{\sqrt{m}}{e} : \frac{\sqrt{2 m}}{e} : \frac{\sqrt{4 m}}{2 e}$

$= 1 : \sqrt{2} : 1$