Problem 27
Determine the electric charge, baryon number, strangeness quantum number, and charm quantum number for the following quark combinations: (a) \(uds\); (b) c\(\overline{u}\); (c) ddd; and (d) d\(\overline{c}\). Explain your reasoning.
Problem 31
The spectrum of the sodium atom is detected in the light from a distant galaxy. (a) If the 590.0-nm line is redshifted to 658.5 nm, at what speed is the galaxy receding from the earth? (b) Use the Hubble law to calculate the distance of the galaxy from the earth.
Problem 37
The 2.728-K blackbody radiation has its peak wavelength at 1.062 mm. What was the peak wavelength at \(t = 700,000\) y when the temperature was 3000 K?
Problem 39
\(\textbf{Radiation Therapy with \)\pi^-\( Mesons.}\) Beams of \(\pi^-\) mesons are used in radiation therapy for certain cancers. The energy comes from the complete decay of the \(\pi^-\) to stable particles. (a) Write out the complete decay of a \(\pi^-\) meson to stable particles. What are these particles? (b) How much energy is released from the complete decay of a single \(\pi^-\) meson to stable particles? (You can ignore the very small masses of the neutrinos.) (c) How many \(\pi^-\) mesons need to decay to give a dose of 50.0 Gy to 10.0 g of tissue? (d) What would be the equivalent dose in part (c) in Sv and in rem? Consult Table 43.3 and use the largest appropriate RBE for the particles involved in this decay.
Problem 40
A proton and an antiproton collide head-on with equal kinetic energies. Two \(\gamma\) rays with wavelengths of 0.720 fm are produced. Calculate the kinetic energy of the incident proton.
Problem 41
Calculate the threshold kinetic energy for the reaction \(p + p \rightarrow p + p + K^+ + K^-\) if a proton beam is incident on a stationary proton target.
Problem 43
Each of the following reactions is missing a single particle. Calculate the baryon number, charge, strangeness, and the three lepton numbers (where appropriate) of the missing particle, and from this identify the particle. (a) \(p + p \rightarrow p + \Lambda^0 + \)? ; (b) \(K^- + n \rightarrow \Lambda^0 +\) ? ; (c) \(p + \overline {p} \rightarrow n + \)?; (d) \(\overline{\nu} _\mu + p \rightarrow n +\)?
Problem 45
The \(\phi\) meson has mass \(1019.4 MeV/c^2\) and a measured energy width of \(4.4 MeV/c^2\). Using the uncertainty principle, estimate the lifetime of the \(\phi\) meson.
Problem 47
One proposed proton decay is \(p^+ \rightarrow e^+ + \pi^0\), which violates both baryon and lepton number conservation, so the proton lifetime is expected to be very long. Suppose the proton half-life were \(1.0 \times 10^{18} y\). (a) Calculate the energy deposited per kilogram of body tissue (in rad) due to the decay of the protons in your body in one year. Model your body as consisting entirely of water. Only the two protons in the hydrogen atoms in each \(H_2O\) molecule would decay in the manner shown; do you see why? Assume that the \(\pi^0\) decays to two \(\gamma\) rays, that the positron annihilates with an electron, and that all the energy produced in the primary decay and these secondary decays remains in your body. (b) Calculate the equivalent dose (in rem) assuming an RBE of 1.0 for all the radiation products, and compare with the 0.1 rem due to the natural background and the 5.0-rem guideline for industrial workers. Based on your calculation, can the proton lifetime be as short as \(1.0 \times 10^{18} y\)?
Problem 52
The \(K^0\) meson has rest energy 497.7 MeV. A \(K^0\) meson moving in the \(+x-\) direction with kinetic energy 225 MeV decays into a \(\pi^+\) and a \(\pi^-\), which move off at equal angles above and below the \(+x-\) axis. Calculate the kinetic energy of the \(\pi^+\) andthe angle it makes with the \(+x-\) axis. Use relativistic expressions for energy and momentum.
