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 the trajectory of proton to that of α -particle

Question

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 the trajectory of proton to that of α -particle is 2 : 1 . The ratio of K p : K α is:

TestHub · Accepted Answer

r = m v q B = p q B m α m p = 4 r p r α = p p q p q α p α = 2 1 p p p a = 2 q p q a = 2 1 2 p p p α = 1 K p K α = p p 2 p α p m α m p = 1 4

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