In Example $44.3$, it was shown that a proton beam with an $800$-GeV beam energy gives an available energy of $38.7$ GeV for collisions with a stationary proton target. In a colliding-beam experiment, what total energy of each beam is needed to give an available energy of $2(38.7$ GeV$)=77.4$ GeV?

Calculate the energy released in the fusion reaction: ${}_2^{3}He{+}_1^{2}H{\to }_2^{4}He{+}_1^{1}H$

A proton and an antiproton annihilate, producing two photons. Find the energy, frequency, and wavelength of each photon if the $p$ and $\overline{p}$ collide head-on, each with an initial kinetic energy of $620$ MeV.

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?

Calculate the minimum beam energy in a proton-proton collider to initiate the $p+p\to p+p+{\eta }^0$ reaction. The rest energy of the ${\eta }^0$ is $547.3$ MeV (see Table $44.3$).

You work for a start-up company that is planning to use antiproton annihilation to produce radioactive isotopes for medical applications. One way to produce antiprotons is by the reaction $p+p\to p+p+p+\bar{p}$ in proton-proton collisions. You first consider a colliding-beam experiment in which the two proton beams have equal kinetic energies. To produce an antiproton via this reaction, what is the required minimum kinetic energy of the protons in each beam?

A $K^{+}$ meson at rest decays into two $p$ mesons. What are the allowed combinations of ${\pi }^0$ , ${\pi }^{+}$, and ${\pi }^{-}$ as decay products?

How much energy is released when a ${\text{µ}}^{-}$ muon at rest decays into an electron and two neutrinos? Neglect the small masses of the neutrinos.

Table $44.3$ shows that a ${\Sigma }^0$ decays into a ${\Lambda }^0$ and a photon. Calculate the energy of the photon emitted in this decay, if the ${\Lambda }^0$ is at rest.