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A proton and an $α$ - particle, having kinetic energies $K_{p}$ and $K_{α}$ respectively, enter into a magnetic field at right angles. The ratio of the radii of trajectory of proton to that of $α$ - particle is 2 : 1. The ratio of $K_{p} : K_{α}$ is:

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Correct option is A

Radius of a particle in the magnetic field is r=mvBq=2mKEBqKE=P22mGiven : rp;rα=2:1 then ⇒rprα=21=mpkpmαkα×qαqp=14kpkα×21⇒KpKα=41

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A proton and an α - particle, having kinetic energies Kp and Kα respectively, enter into a magnetic field at right angles. The ratio of the radii of trajectory of proton to that of α - particle is 2 : 1. The ratio of Kp:Kα is:

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Ready to Test Your Skills?

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A proton and an $α$ - particle, having kinetic energies $K_{p}$ and $K_{α}$ respectively, enter into a magnetic field at right angles. The ratio of the radii of trajectory of proton to that of $α$ - particle is 2 : 1. The ratio of $K_{p} : K_{α}$ is: