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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

What is the wavelength of an \({\rm{50 - GeV}}\) electron, which is produced at SLAC? This provides an idea of the limit to the detail it can probe.

(a) Show that the conjectured decay of the proton, \({\rm{p}} \to {\pi ^{\rm{0}}}{\rm{ + }}{{\rm{e}}^{\rm{ + }}}\), violates conservation of baryon number and conservation of lepton number.

(b) What is the analogous decay process for the antiproton?

Identify evidence for electroweak unification.

The mass of a theoretical particle that may be associated with the unification of the electroweak and strong forces is\[{\rm{1}}{{\rm{0}}^{{\rm{14}}}}{\rm{ GeV/}}{{\rm{c}}^{\rm{2}}}\]. (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 纬 would have to be.)

Accelerators such as the Triangle Universities Meson Facility (TRIUMF) in British Columbia produce secondary beams of pions by having an intense primary proton beam strike a target. Such "meson factories" have been used for many years to study the interaction of pions with nuclei and, hence, the strong nuclear force. One reaction that occurs is\({{\rm{\pi }}^{\rm{ + }}}{\rm{ + p}} \to {{\rm{\Delta }}^{{\rm{ + + }}}} \to {{\rm{\pi }}^{\rm{ + }}}{\rm{ + p}}\), where the \({{\rm{\Delta }}^{{\rm{ + + }}}}\)is a very short-lived particle. The graph in Figure \({\rm{33}}{\rm{.26}}\)shows the probability of this reaction as a function of energy. The width of the bump is the uncertainty in energy due to the short lifetime of the\({{\rm{\Delta }}^{{\rm{ + + }}}}\).

(a) Find this lifetime.

(b) Verify from the quark composition of the particles that this reaction annihilates and then re-creates a d quark and a \({\rm{\bar d}}\)antiquark by writing the reaction and decay in terms of quarks.

(c) Draw a Feynman diagram of the production and decay of the \({{\rm{\Delta }}^{{\rm{ + + }}}}\)showing the individual quarks involved.
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