Additional Problems

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

$\begin{array}{c}\text{(a)}\text{p}+\stackrel{\text{−}}{\text{p}}\to \text{n}+?\hfill \\ \text{(b)}\text{p}+\text{p}\to \text{p}+{\text{Λ}}^0+?\hfill \\ \text{(c)}{\pi }^{–}+\text{p}\to {\text{Σ}}^{\text{−}}+?\hfill \\ \text{(d)}{\text{K}}^{\text{−}}+\text{n}\to {\text{Λ}}^0+?\hfill \\ \text{(e)}{\tau }^{+}\to {\text{e}}^{+}+{\nu }_{\text{e}}+?\hfill \\ \text{(f)}{\stackrel{\text{−}}{\nu }}_{\text{e}}+\text{p}\to \text{n}+?\hfill \end{array}$

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.)

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 $5.0\times {10}^5\text{km}$ 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.

(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 $2\times {10}^{10}$ years old?