Problem 4
A proton and an antiproton annihilate, producing two photons. Find the energy, frequency, and wavelength of each photon (a) if the p and \(\overline{p}\) are initially at rest and (b) if the p and \(\overline{p}\) collide head-on, each with an initial kinetic energy of 620 MeV.
Problem 6
Estimate the range of the force mediated by an \(\omega$$^0\) meson that has mass 783 MeV/\(c$$^2\).
Problem 7
The starship \(Enterprise\), of television and movie fame, is powered by combining matter and antimatter. If the entire 400-kg antimatter fuel supply of the \(Enterprise\) combines with matter, how much energy is released? How does this compare to the U.S. yearly energy use, which is roughly \(1.0 \times 10^{20}\) J ?
Problem 9
Deuterons in a cyclotron travel in a circle with radius 32.0 cm just before emerging from the dees. The frequency of the applied alternating voltage is 9.00 MHz. Find (a) the magnetic field and (b) the kinetic energy and speed of the deuterons upon emergence.
Problem 10
The magnetic field in a cyclotron that accelerates protons is 1.70 T. (a) How many times per second should the potential across the dees reverse? (This is twice the frequency of the circulating protons.) (b) The maximum radius of the cyclotron is 0.250 m. What is the maximum speed of the proton? (c) Through what potential difference must the proton be accelerated from rest to give it the speed that you calculated in part (b)?
Problem 11
(a) A high-energy beam of alpha particles collides with a stationary helium gas target. What must the total energy of a beam particle be if the available energy in the collision is 16.0 GeV? (b) If the alpha particles instead interact in a colliding-beam experiment, what must the energy of each beam be to produce the same available energy?
Problem 18
How much energy is released when a \(\mu^-\) muon at rest decays into an electron and two neutrinos? Neglect the small masses of the neutrinos.
Problem 23
In which of the following decays are the three lepton numbers conserved? In each case, explain your reasoning. (a) \(\mu^-\rightarrow e^- + \nu_e + \overline{\nu}_\mu\); (b) \(\tau^-\rightarrow e^- + \overline{\nu}_e + \overline {\nu} _\tau\); (c) \(\pi^+ \rightarrow e^+ + \gamma\); (d) \(n \rightarrow p + e^- + \overline{\nu}_e\).
Problem 24
Which of the following reactions obey the conservation of baryon number? (a) \(p + p \rightarrow p + e^+\); (b) \(p + n \rightarrow 2e^+ + e^-\); (c) \(p \rightarrow n + e^- + \overline{\nu}_e\); (d) \(p + \overline{p} \rightarrow 2\gamma\).
Problem 25
In which of the following reactions or decays is strangeness conserved? In each case, explain your reasoning. (a) \(K^+ \rightarrow \mu^+ + \nu_\mu\); (b) \(n + K^+ \rightarrow p + \pi^0\); (c) \(K^+ + K^- \rightarrow \pi^0 + \pi^0\); (d) \(p + K^- \rightarrow \Lambda^0 + \pi^0\).
