Question

Quarks and gluons are fundamental particles that will be discussed in Chapter 44. A proton, which is a bound state of two up quarks and a down quark, has a rest mass of mp=1.67×10−27 kg.mp=1.67×10−27 kg. This is significantly greater than the sum of the rest mass of the up quarks, which is mu=4.12×10−30 kgmu=4.12×10−30 kg each, and the rest mass of the down quark, which is md=8.59×10−30 kg.md=8.59×10−30 kg. Suppose we (incorrectly) model the rest energy of the proton mpc2mpc2 as derived from the kinetic energy of the three quarks, and we split that energy equally among them. (a) Estimate the Lorentz factor γ=(1−υ2/c2)−1/2γ=(1−υ2/c2)−1/2 for each of the up quarks using Eq. (37.36). (b) Similarly estimate the Lorentz factor γγ for the down quark. (c) Are the corresponding speeds υuυu and υdυd greater than 99% of the speed of light? (d) More realistically, the quarks are held together by massless gluons, which mediate the strong nuclear interaction. Suppose we model the proton as the three quarks, each with a speed of 0.90c,0.90c, with the remainder of the proton rest energy supplied by gluons. In this case, estimate the percentage of the proton rest energy associated with gluons. (e) Model a quark as oscillating with an average speed of 0.90c0.90c across the diameter of a proton, 1.7×10−15 m.1.7×10−15 m. Estimate the frequency of that motion.

Answer 1