1. Intro to Physics Units

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.

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?

What is the total kinetic energy of the decay products when an upsilon particle at rest decays to $r^{+}+r^{-}$?

The spectrum of the sodium atom is detected in the light from a distant galaxy. Use the Hubble law to calculate the distance of the galaxy from the earth.

Show that the product RC has units of s.

Make a graph of the kinetic energy versus momentum for (a) a particle of nonzero mass, and (b) a particle with zero mass.