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?

Two equal-energy photons collide head-on and annihilate each other, producing a ${\text{µ}}^{+}{\text{µ}}^{-}$ pair. The muon mass is given in terms of the electron mass in Section $44.1$. Calculate the maximum wavelength of the photons for this to occur. If the photons have this wavelength, describe the motion of the ${\text{µ}}^{+}$ and immediately after they are produced.

A proton and an antiproton annihilate, producing two photons. Find the energy, frequency, and wavelength of each photon if the $p$ and $\bar{p}$ are initially at rest.

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.

An electron with a total energy of $30.0$ GeV collides with a stationary positron. What is the available energy?

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 the magnetic field.

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?

What is the speed of a proton that has total energy $1000$ GeV?

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.

If a ${\Sigma }^{+}$ at rest decays into a proton and a ${\pi }^0$, what is the total kinetic energy of the 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) $p+K^{-}\to {\Lambda }^0+{\pi }^0$

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. If the $590.0$-nm line is redshifted to $658.5$ nm, at what speed is the galaxy receding from the earth?

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.