### Additional Problems

Experimental results suggest that a muon decays to an electron and photon. How is this possible?

Each of the following reactions is missing a single particle. Identify the missing particle for each reaction.

$\begin{array}{c}\text{(a)}\phantom{\rule{0.2em}{0ex}}\text{p}+\stackrel{\text{\u2212}}{\text{p}}\to \text{n}+?\hfill \\ \text{(b)}\phantom{\rule{0.2em}{0ex}}\text{p}+\text{p}\to \text{p}+{\text{\Lambda}}^{0}+?\hfill \\ \text{(c)}\phantom{\rule{0.2em}{0ex}}{\pi}^{\u2013}+\text{p}\to {\text{\Sigma}}^{\text{\u2212}}+?\hfill \\ \text{(d)}\phantom{\rule{0.2em}{0ex}}{\text{K}}^{\text{\u2212}}+\text{n}\to {\text{\Lambda}}^{0}+?\hfill \\ \text{(e)}\phantom{\rule{0.2em}{0ex}}{\tau}^{+}\to {\text{e}}^{+}+{\nu}_{\text{e}}+?\hfill \\ \text{(f)}\phantom{\rule{0.2em}{0ex}}{\stackrel{\text{\u2212}}{\nu}}_{\text{e}}+\text{p}\to \text{n}+?\hfill \end{array}$

Because of energy loss due to synchrotron radiation in the LHC at CERN, only 5.00 MeV is added to the energy of each proton during each revolution around the main ring. How many revolutions are needed to produce 7.00-TeV (7000 GeV) protons, if they are injected with an initial energy of 8.00 GeV?

A proton and an antiproton collide head-on, with each having a kinetic energy of 7.00 TeV (such as in the LHC at CERN). How much collision energy is available, taking into account the annihilation of the two masses? (Note that this is not significantly greater than the extremely relativistic kinetic energy.)

When an electron and positron collide at the SLAC facility, they each have 50.0-GeV kinetic energies. What is the total collision energy available, taking into account the annihilation energy? Note that the annihilation energy is insignificant, because the electrons are highly relativistic.

The core of a star collapses during a supernova, forming a neutron star. Angular momentum of the core is conserved, so the neutron star spins rapidly. If the initial core radius is $5.0\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{5}\phantom{\rule{0.2em}{0ex}}\text{km}$ and it collapses to 10.0 km, find the neutron star’s angular velocity in revolutions per second, given the core’s angular velocity was originally 1 revolution per 30.0 days.

Using the solution from the previous problem, find the increase in rotational kinetic energy, given the core’s mass is 1.3 times that of our Sun. Where does this increase in kinetic energy come from?

(a) What Hubble constant corresponds to an approximate age of the universe of ${10}^{10}$ y? To get an approximate value, assume the expansion rate is constant and calculate the speed at which two galaxies must move apart to be separated by 1 Mly (present average galactic separation) in a time of ${10}^{10}$ y. (b) Similarly, what Hubble constant corresponds to a universe approximately $2\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{10}$ years old?