(II) Make a graph of the kinetic energy versus momentum for (a) a particle of nonzero mass, and (b) a particle with zero mass.

Verified step by step guidance

1. First, recall the relationship between kinetic energy (K) and momentum (p) for a particle. The kinetic energy is given by K = \frac{p^2}{2m}, where p is the momentum and m is the mass of the particle.
2. For a particle of nonzero mass (a), plot the graph using the equation K = \frac{p^2}{2m}. This equation shows that kinetic energy is proportional to the square of the momentum. As momentum increases, kinetic energy increases quadratically. The graph will be a parabola opening upwards starting from the origin (0,0).
3. For a particle with zero mass (b), such as a photon, the situation is different because the standard formula K = \frac{p^2}{2m} becomes undefined as m approaches zero. Instead, use the relativistic energy-momentum relation E^2 = (pc)^2 + (mc^2)^2. For zero mass, this simplifies to E = pc, where E is the total energy which, for a massless particle, is equivalent to its kinetic energy.
4. Plot the graph for a particle with zero mass using the equation K = pc. This shows a linear relationship between kinetic energy and momentum. The graph will be a straight line passing through the origin with a slope equal to the speed of light c.
5. From these graphs, you can compare how kinetic energy depends on momentum for particles with mass and without mass. The parabolic shape for particles with mass indicates a quadratic dependence, while the linear shape for massless particles shows a direct proportionality.