Why may it be advantageous for a scientist to discover particle interactions that defy a recognised particle conservation law?

(a) What is the approximate velocity of a galaxy near the edge of the known universe, some $10 \mathrm{Gly}$ away, relative to us? (b) What is the fraction of the speed of light? It is worth noting that we have observed galaxies moving away from us at speeds greater than $0.9 c$.

Our solar system revolves around the Milky Way Galaxy's nucleus. How many years does it take for one revolution in a circular orbit with a radius of 30,000 ly and an orbital speed of $250 \mathrm{~km} / \mathrm{s}$? This is an approximation, assuming constant speed and circular orbit, but it represents the time it takes our system and local stars to complete one revolution around the galaxy.

How far away are galaxies moving away from us at $2.0 \%$ of the speed of light on average?

How fast and in which direction should we expect a galaxy that is $153 \mathrm{Mpc}$ away from us to move?

A galaxy is 10 Mpc away from our solar system. (a) What is the galaxy's recessional velocity? (b) How much is the starlight from this galaxy redshifted (what is its z value)?

What is the distance of a distant galaxy from an Earth-bound observer if its speed is $0.99 c$?

Assume that you are planning a proton decay experiment and that you can identify 50% of proton decays in a water tank. a. In order to observe one degradation per month, assuming a lifetime of $10^{31} \mathrm{y}$, how many kilogrammes of water would you need? (b) How much water, in cubic metres, is this? (c) How long would it take to witness a single proton decay on average if the actual lifetime was $10^{33} \mathrm{y}$?

How do we ascertain whether a particle reaction or decay takes place in general?

The negative pion's fundamental decay mode is $\pi^{-} \rightarrow \mu^{-}+\bar{\nu} \mu$.  (a) How much energy is released in this decay,  $\mathrm{MeV}$? (b) Given that the$\pi^{-}$ is at rest as it decays, how much energy does each of the decay products get under the principle of conservation of momentum? You can assume that the muon antineutrino has the same momentum as a photon, $p=E / c$ and is massless.

What is the wavelength of an electron that is generated at SLAC and has a mass of $50-\mathrm{GeV}$? This gives a general indication of how much detail it can explore.

What is the energy of each $\gamma$ ray produced in the reaction of a neutral pion decaying at rest, assuming momentum conservation

$$\pi^0 \rightarrow \gamma+\gamma$$

(a) The electroweak force mediates the following decay:

$$\mathrm{p} \rightarrow \mathrm{n}+\mathrm{e}^{+}+v_{\mathrm{e}}$$

Draw the Feynman diagram for the decay. (b)The electroweak force mediates the dispersion of the following particles:

$$v_e+\mathrm{e}^{-} \rightarrow v_e+\mathrm{e}^{-}$$

Draw the Feynman diagram for the scattering.

Estimate the range of a weak nuclear decay involving a graviton using the Heisenberg uncertainty principle.