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Chapter 33: Q11PE (page 1212)

A proton and an antiproton collide head-on, with each having a kinetic energy of 7.00TeV (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.)

Short Answer

Expert verified

The total collision energy of the annihilation of the two masses is \(14\;{\rm{TeV}}\).

Step by step solution

01

Definition of Energy

Law of conservation of energy states that the energy content of the universe remains constant. Energy can neither be created nor destroyed, it just changes its form from one to another.

02

Finding required energy

The total energy of the particle is the sum of the kinetic energy and the rest energy, mc2. Thecollision energy,

\({\rm{E}}\)=\({\rm{2}}\left( {{\rm{K}}{\rm{.E + m}}{{\rm{c}}^{\rm{2}}}} \right)\)

\(\begin{array}{}E = 2\left( {7\;{\rm{TeV}} + \left( {9.38 \times {{10}^{ - 4}}\;{\rm{TeV}}} \right)} \right)\\ = 14\;{\rm{TeV}}\end{array}\)

The total collision energy of the annihilation of the two massesis\(14\;{\rm{TeV}}\).

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Most popular questions from this chapter

Explain how conservation of baryon number is responsible for conservation of total atomic mass (total number of nucleons) in nuclear decay and reactions.

There are particles called bottom mesons or \({\rm{B}}\)-mesons. One of them is the \({{\rm{B}}^{\rm{ - }}}\)meson, which has a single negative charge; its baryon number is zero, as are its strangeness, charm, and topness. It has a bottomness of \({\rm{ - 1}}\). What is its quark configuration?

In supernovas, neutrinos are produced in huge amounts. They were detected from the \({\rm{1987 A}}\) supernova in the Magellanic Cloud, which is about \({\rm{120,000}}\) light years away from the Earth (relatively close to our Milky Way galaxy). If neutrinos have a mass, they cannot travel at the speed of light, but if their mass is small, they can get close.

(a) Suppose a neutrino with a \({\rm{7 - eV/}}{{\rm{c}}^{\rm{2}}}\) mass has a kinetic energy of \({\rm{700 KeV}}\). Find the relativistic quantity \(\gamma {\rm{ = }}\frac{{\rm{1}}}{{\sqrt {{\rm{1 - }}{{{{\rm{\nu }}^{\rm{2}}}} \mathord{\left/ {\vphantom {{{{\rm{\nu }}^{\rm{2}}}} {{{\rm{c}}^{\rm{2}}}}}} \right. \\} {{{\rm{c}}^{\rm{2}}}}}} }}\) for it.

(b) If the neutrino leaves the \({\rm{1987 A}}\) supernova at the same time as a photon and both travel to Earth, how much sooner does the photon arrive? This is not a large time difference, given that it is impossible to know which neutrino left with which photon and the poor efficiency of the neutrino detectors. Thus, the fact that neutrinos were observed within hours of the brightening of the supernova only places an upper limit on the neutrino’s mass. (Hint: You may need to use a series expansion to find \({\rm{v}}\) for the neutrino, since it \(\gamma \) is so large.)

The primary decay mode for the negative pion \({\pi ^{\rm{ - }}} \to {{\rm{\mu }}^{\rm{ - }}}{\rm{ + }}{{\rm{\bar \upsilon }}_{\rm{\mu }}}\).

(a) What is the energy release in \({\rm{MeV}}\) in this decay?

(b) Using conservation of momentum, how much energy does each of the decay products receive, given the \({\pi ^{\rm{ - }}}\) is at rest when it decays? You may assume the muon antineutrino is massless and has momentum \(p = \frac{{{E_\nu }}}{c}\), just like a photon.

(a) Is the decay \({\sum ^{\rm{ - }}} \to {\rm{n + }}{\pi ^{\rm{ - }}}\) possible considering the appropriate conservation laws? State why or why not.

(b) Write the decay in terms of the quark constituents of the particles.
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