Chapter 33: Particle PhysicsContent check — College Physics, Chapter 33: Particle Physics

A virtual particle having an approximate mass of ${\text{10}}^{\text{14}}\text{GeV/}{c}^2$ may be associated with the unification of the strong and electroweak forces. For what length of time could this virtual particle exist (in temporary violation of the conservation of mass-energy as allowed by the Heisenberg uncertainty principle)?

Another component of the strong nuclear force is transmitted by the exchange of virtual K-mesons. Taking K-mesons to have an average mass of $\text{495}\text{MeV/}{c}^2$, what is the approximate range of this component of the strong force?

(a) Find the ratio of the strengths of the weak and electromagnetic forces under ordinary circumstances.

(b) What does that ratio become under circumstances in which the forces are unified?

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 0.100 c leave in a bubble chamber if it is created there and lives for $2\text{.}\text{60}\times {\text{10}}^{-8}\text{s}$? (Those moving faster or living longer may escape the detector before decaying.)

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?

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 ${\pi }^0$ is its own antiparticle and decays in the following manner: ${\pi }^0\to \gamma +\gamma$. What is the energy of each $\gamma$ ray if the ${\pi }^0$ is at rest when it decays?

The mass of a theoretical particle that may be associated with the unification of the electroweak and strong forces is ${\text{10}}^{\text{14}}\text{GeV/}{c}^2$.

(a) How many proton masses is this?

(b) How many electron masses is this? (This indicates how extremely relativistic the accelerator would have to be in order to make the particle, and how large the relativistic quantity $\gamma$ would have to be.)

The decay mode of the positive tau is ${\tau }^{+}\to$ ${\mu }^{+}+$ ${\nu }_{\mu }+$ ${\stackrel{-}{\nu }}_{\tau }$.

(a) What energy is released?

(b) Verify that charge and lepton family numbers are conserved.

(c) The ${\tau }^{+}$ is the antiparticle of the ${\tau }^{-}$.Verify that all the decay products of the ${\tau }^{+}$ are the antiparticles of those in the decay of the ${\tau }^{-}$ given in the text.

(a) What is the uncertainty in the energy released in the decay of a ${\pi }^0$ due to its short lifetime?

(b) What fraction of the decay energy is this, noting that the decay mode is ${\pi }^0\to \gamma +\gamma$ (so that all the ${\pi }^0$ mass is destroyed)?

(a) Verify from its quark composition that the ${\text{Δ}}^{+}$ particle could be an excited state of the proton.

(b) There is a spread of about 100 MeV in the decay energy of the ${\text{Δ}}^{+}$, interpreted as uncertainty due to its short lifetime. What is its approximate lifetime?

(c) Does its decay proceed via the strong or weak force?

The reaction ${\pi }^{+}+p\to {\text{Δ}}^{\text{++}}$ (described in the preceding problem) takes place via the strong force. (a) What is the baryon number of the ${\text{Δ}}^{\text{++}}$ particle?

(b) Draw a Feynman diagram of the reaction showing the individual quarks involved.

Repeat the previous problem for the decay mode ${\Omega }^{-}\to {\text{Λ}}^0+K^{-}.$

One decay mode for the eta-zero meson is ${\eta }^0\to {\pi }^0+{\pi }^0$.

(a) Write the decay in terms of the quark constituents.

(b) How much energy is released?

(c) What is the ultimate release of energy, given the decay mode for the pi zero is ${\pi }^0\to \gamma +\gamma$?

Is the decay ${\mu }^{-}\to e^{-}+{\nu }_e+{\nu }_{\mu }$ possible considering the appropriate conservation laws? State why or why not.

(a) Is the decay ${\text{Σ}}^{-}\to n+{\pi }^{-}$ possible considering the appropriate conservation laws? State why or why not. (b) Write the decay in terms of the quark constituents of the particles.

(a) Three quarks form a baryon. How many combinations of the six known quarks are there if all combinations are possible?

(b) This number is less than the number of known baryons. Explain why.

Verify the quantum numbers given for the ${\Omega }^{+}$ in Table 33.2 by adding the quantum numbers for its quark constituents as inferred from Table 33.4.

(a) How much energy would be released if the proton did decay via the conjectured reaction $p\to {\pi }^0+e^{+}$?

(b) Given that the ${\pi }^0$ decays to two $\gamma$ s and that the $e^{+}$ will find an electron to annihilate, what total energy is ultimately produced in proton decay?

(c) Why is this energy greater than the proton’s total mass (converted to energy)?

There are particles called D-mesons. One of them is the $D^{+}$ meson, which has a single positive charge and a baryon number of zero, also the value of its strangeness, topness, and bottomness. It has a charm of $+1.$ What is its quark configuration?

(a) What particle has the quark composition $\stackrel{-}{u}\stackrel{-}{u}\stackrel{-}{d}$?

(b) What should its decay mode be?

Integrated Concepts

The intensity of cosmic ray radiation decreases rapidly with increasing energy, but there are occasionally extremely energetic cosmic rays that create a shower of radiation from all the particles they create by striking a nucleus in the atmosphere as seen in the figure given below. Suppose a cosmic ray particle having an energy of ${\text{10}}^{\text{10}}\text{GeV}$ converts its energy into particles with masses averaging $\text{200}\text{MeV/}{c}^2$. (a) How many particles are created? (b) If the particles rain down on a $1\text{.}{\text{00-km}}^2$ area, how many particles are there per square meter?

Integrated Concepts

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.

Integrated Concepts

The primary decay mode for the negative pion is ${\pi }^{-}\to {\mu }^{-}+{\stackrel{-}{\nu }}_{\mu }$. (a) What is the energy release in MeV in this decay? (b) Using conservation of momentum, how much energy does each of the decay products receive, given the ${\pi }^{-}$ is at rest when it decays? You may assume the muon antineutrino is massless and has momentum $p=E/c$, just like a photon.

Integrated Concepts

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 ${\text{10}}^{\text{31}}\text{y}$? (b) How many cubic meters of water is this? (c) If the actual lifetime is ${\text{10}}^{\text{33}}\text{y}$, how long would you have to wait on an average to see a single proton decay?

Critical Thinking (a) How much mass is converted to energy when a proton and antiproton annihilate each other? (b) How much energy is produced in the conversion above? (c) If energy were to produce a proton-antiproton pair, how much energy would this take? (d) What characteristic other than one being antimatter is different for a proton and an antiproton?