Two particles X and Y carrying the same charge are accelerated through an identical potential difference before entering a region with a uniform magnetic field. They describe circular paths of radii R₁ and R₂ respectively. The ratio of the mass of X to the mass of Y is

Step-by-step solution

The kinetic energy gained by a particle of charge q accelerated through a potential difference V is K = qV . The momentum of the particle is p = 2mK = 2mqV . When the particle enters a uniform magnetic field B perpendicularly, the radius of its circular path is given by R = p qB = 2mqV qB . Squaring both sides, we get R^2 = 2mV qB^2 , which gives m = qB^2 R^2 2V . Since q , V , and B are the same for both particles X and Y , the mass is directly proportional to the square of the radius, m R^2 . Therefore, the ratio