Problems

If $1.0\times {10}^{30}\text{MeV}$ of energy is released in the annihilation of a sphere of matter and antimatter, and the spheres are equal mass, what are the masses of the spheres?

What is the total kinetic energy carried away by the particles of the following decays?
$\begin{array}{}\\ \\ (\text{a}){\pi }^0\to \gamma +\gamma \hfill \\ (\text{b}){\text{K}}^0\to {\pi }^{+}+{\pi }^{\text{−}}\hfill \\ (\text{c}){\Sigma }^{+}\to n+{\pi }^{+}\hfill \\ (\text{d}){\Sigma }^0\to {\Lambda }^0+\gamma .\hfill \end{array}$

Which of the following reactions cannot because the law of conservation of strangeness is violated?

$\begin{array}{ccc}(\text{a})\text{p}+\text{n}\to \text{p}+\text{p}+{\pi }^{\text{−}}\hfill & & (\text{e}){\text{K}}^{\text{−}}+\text{p}\to {\text{Ξ}}^0+{\text{K}}^{+}+{\pi }^{\text{−}}\hfill \\ (\text{b})\text{p}+\text{n}\to \text{p}+\text{p}+{\text{K}}^{\text{−}}\hfill & & (\text{f}){\text{K}}^{\text{−}}+\text{p}\to {\text{Ξ}}^0+{\pi }^{\text{−}}+{\pi }^{\text{−}}\hfill \\ (\text{c}){\text{K}}^{\text{−}}+\text{p}\to {\text{K}}^{\text{−}}+{\sum }^{+}\hfill & & (\text{g}){\pi }^{+}+\text{p}\to {\Sigma }^{+}+{\text{K}}^{+}\hfill \\ (\text{d}){\pi }^{\text{−}}+\text{p}\to {\text{K}}^{+}+{\sum }^{\text{−}}\hfill & & (\text{h}){\pi }^{\text{−}}+\text{n}\to {\text{K}}^{\text{−}}+{\text{Λ}}^0\hfill \end{array}$

Each of the following strong nuclear reactions is forbidden. Identify a conservation law that is violated for each one.

$\begin{array}{}\\ \text{(a)}\text{p}+\stackrel{\text{−}}{\text{p}}\to \text{p}+\text{n}+\stackrel{\text{−}}{\text{p}}\hfill \\ \text{(b)}\text{p}+\text{n}\to \text{p}+\stackrel{\text{−}}{\text{p}}+\text{n}+{\pi }^{+}\hfill \\ \text{(c)}{\pi }^{\text{−}}+\text{p}\to {\Sigma }^{+}+{\text{K}}^{\text{−}}\hfill \\ \text{(d)}{\text{K}}^{\text{−}}+\text{p}\to {\text{Λ}}^0+\text{n}\hfill \end{array}$

Based on the quark composition of a neutron, show that is charge is 0.

Mesons are formed from the following combinations of quarks (subscripts indicate color and $AR=\text{antired}$): $(d_{\text{R}},{\stackrel{\text{−}}{d}}_{\text{AR}})$, ($s_{\text{G}},{\stackrel{\text{−}}{u}}_{\text{AG}}$), and ($s_{\text{R}},{\stackrel{\text{−}}{s}}_{\text{AR}}$).

(a) Determine the charge and strangeness of each combination. (b) Identify one or more mesons formed by each quark-antiquark combination.

Experimental results indicate an isolate particle with charge $+2\text{/}3$—an isolated quark. What quark could this be? Why would this discovery be important?

A charged particle in a 2.0-T magnetic field is bent in a circle of radius 75 cm. What is the momentum of the particle?

Derive the equation $p=0.3Br$ using the concepts of centripetal acceleration (Motion in Two and Three Dimensions) and relativistic momentum (Relativity)

At full energy, protons in the 2.00-km-diameter Fermilab synchrotron travel at nearly the speed of light, since their energy is about 1000 times their rest mass energy. (a) How long does it take for a proton to complete one trip around? (b) How many times per second will it pass through the target area?

What length track does a ${\pi }^{+}$ traveling at 0.100c leave in a bubble chamber if it is created there and lives for $2.60\times {10}^{\mathrm{-8}}\text{s}$? (Those moving faster or living longer may escape the detector before decaying.)

Using the Heisenberg uncertainly principle, determine the range of the weak force if this force is produced by the exchange of a Z boson.

(a) The following decay is mediated by the electroweak force:

$\text{p}\to \text{n}+{\text{e}}^{+}+{\upsilon }_{\text{e}}.$

Draw the Feynman diagram for the decay.

(b) The following scattering is mediated by the electroweak force:

${\upsilon }_e+{\text{e}}^{\text{−}}\to {\upsilon }_e+{\text{e}}^{\text{−}}.$

Draw the Feynman diagram for the scattering.

What is the wavelength of a 50-GeV electron, which is produced at SLAC? This provides an idea of the limit to the detail it can probe.

Suppose you are designing a proton decay experiment and you can detect 50 percent of the proton decays in a tank of water. (a) How many kilograms of water would you need to see one decay per month, assuming a lifetime of ${10}^{31}\text{y?}$ (b) How many cubic meters of water is this? (c) If the actual lifetime is ${10}^{33}\text{y}$, how long would you have to wait on an average to see a single proton decay?

The distance of a galaxy from our solar system is 10 Mpc. (a) What is the recessional velocity of the galaxy? (b) By what fraction is the starlight from this galaxy redshifted (that is, what is its z value)?

On average, how far away are galaxies that are moving away from us at $2.0\text{\%}$ of the speed of light?

(a) What is the approximate velocity relative to us of a galaxy near the edge of the known universe, some 10 Gly away? (b) What fraction of the speed of light is this? Note that we have observed galaxies moving away from us at greater than 0.9c.

The Andromeda Galaxy is the closest large galaxy and is visible to the naked eye. Estimate its brightness relative to the Sun, assuming it has luminosity ${10}^{12}$ times that of the Sun and lies 0.613 Mpc away.