A proton and a deutron (q = +e, m = 2.0u) having same kinetic energies enter a region of uniform magnetic field B, moving perpendicular to B. The ratio of the radius r(d) of deutron path to the radius r(p) of the proton path is :
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Question

A proton and a deutron (q = +e, m = 2.0u) having same kinetic energies enter a region of uniform magnetic field B, moving perpendicular to B. The ratio of the radius r(d) of deutron path to the radius r(p) of the proton path is :

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G1 Physics · Accepted Answer

For a charged particle moving perpendicular to a uniform magnetic field: r = mv/(qB) Using: K = ½mv² we get: r = √(2mK)/(qB) For the same kinetic energy and same charge magnitude: r ∝ √m Therefore: r(d)/r(p) = √(m(d)/m(p)) = √2 Hence: r(d) : r(p) = √2 : 1