A proton and an α - particle (with their masses in the ratio of 1 : 4 and charges in the ratio of 1 : 2 ) are accelerated from rest through a potential difference V . If a uniform magnetic field B is

Question

A proton and an α - particle (with their masses in the ratio of 1 : 4 and charges in the ratio of 1 : 2 ) are accelerated from rest through a potential difference V . If a uniform magnetic field B is set up perpendicular to their velocities, the ratio of the radii r p : r α of the circular paths described by them will be:

TestHub · Accepted Answer

The kinetic energy of a charge q of mass m in potential is given by, 1 2 m v 2 = q V m v = 2 m q V Then, the radius of the charge will be, r = 2 m q V q B ⇒ r ∝ m q Hence, the ratio of radius of proton to α -particle, r p r α = 1 4 × 2 1 = 1 2 .

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