Assertion (A): If O²⁻ and H⁺ ions enter perpendicular to the same magnetic field with equal momentum, the path of O²⁻ has a smaller radius of curvature than that of H⁺. Reason (R): A proton and an electron having the same momentum form paths of different radii in the same magnetic field because their masses are different. Choose the correct answer.
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Question

Assertion (A): If O²⁻ and H⁺ ions enter perpendicular to the same magnetic field with equal momentum, the path of O²⁻ has a smaller radius of curvature than that of H⁺. Reason (R): A proton and an electron having the same momentum form paths of different radii in the same magnetic field because their masses are different. Choose the correct answer.

Options

G1 Physics · Accepted Answer

For a charged particle entering a uniform magnetic field perpendicular to its velocity, r = p/(|q|B). For equal momentum p and the same B, radius depends only on the magnitude of charge. For O²⁻, |q| = 2e, while for H⁺, |q| = e. Thus, r(O²⁻) = p/(2eB) and r(H⁺) = p/(eB). Therefore O²⁻ has the smaller radius. Assertion A is true. For a proton and electron with the same momentum, |q| is e for both. Hence r = p/(eB) is the same for both, independent of mass. Therefore the Reason is false. Correct…