Final answer:
The ratio of the kinetic energies of an alpha particle and a proton, given the same linear momentum, is 4:1, which is inversely proportional to their mass ratio.
Step-by-step explanation:
The question revolves around finding the ratio of the kinetic energies of an alpha particle and a proton given that they have the same linear momentum. Kinetic energy (KE) can be expressed in terms of momentum (p) and mass (m) as KE = p2 / (2m). Since both particles have the same momentum, the ratio of their kinetic energies will be inversely proportional to their masses.
An alpha particle is a helium nucleus which contains 2 protons and 2 neutrons, so its mass is approximately 4 times that of a proton. Therefore, the kinetic energy of the proton will be greater due to its smaller mass. Let's denote KEα as the kinetic energy of the alpha particle and KEp as the kinetic energy of the proton. Hence, the ratio of their kinetic energies will be KEp / KEα = mα / mp = 4:1, making the correct answer (c).