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.

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?

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.

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

In which of the following reactions or decays is strangeness conserved? In each case, explain your reasoning.

(a) $K^{+}+{\mu }^{+}+{\nu }_{\mu }$

(b) $n+K^{+}\to p+{\pi }^0$

(c) $K^{+}+K^{-}\to {\pi }^0+{\pi }^0$

(d) $p+K^{-}\to {\Lambda }^0+{\pi }^0$

Table $44.3$ shows that a $Σ^0$ decays into a ${\Lambda }^0$ and a photon. What is the magnitude of the momentum of the photon? Is it reasonable to ignore the final momentum and kinetic energy of the ${\Lambda }^0$? Explain.

If a ${\Sigma }^{+}$ at rest decays into a proton and a ${\pi }^0$, what is the total kinetic energy of the decay products?