A proton and an alpha particle, both are moving with same initial velocity, perpendicular to uniform magnetic field of 1 T. Find the ratio of radii of circles described by the alpha particle and the proton.

Explanation

The radius of a charged particle's path in a magnetic field is given by the formula r = (mv) / (qB), where m is the mass, v is the velocity, q is the charge, and B is the magnetic field strength. For a proton, m = m_p, q = e. For an alpha particle, m = 4m_p, q = 2e. Given the same velocity and magnetic field, the radius for the proton is r_p = (m_p * v) / (e * B) and for the alpha particle is r_alpha = (4m_p * v) / (2e * B). Simplifying, r_alpha / r_p = 2. Thus, the radius of the alpha particle's path is twice that of the proton's path. This makes Option A correct. Options B, C, and D are incorrect as they do not accurately reflect the differences in mass and charge between the proton and alpha particle.