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Chapter 33: Q12PE (page 1212)

When an electron and positron collide at the SLAC facility, they each have 50.0GeV 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.

Short Answer

Expert verified

The total collision energy available, taking into account the annihilation energyis 100 GeV.

Step by step solution

01

Definition of Energy

Energy of a particle by virtue of its motion is known as kinetic energy. If the particle is moving at relativistic speeds, then relativistic correction should also be considered to get the accurate value of kinetic energy.

02

Finding required energy

The total energy of the particle is the sum of the kinetic energy and the rest energy, mc2. So, the collision energy, E, equals \({\rm{2}}\left( {{\rm{K}}{\rm{.E + m}}{{\rm{c}}^{\rm{2}}}} \right)\)

\(\begin{align}{}E &= 2\left( {\left( {50\;{\rm{GeV}}} \right) + \left( {5.11 \times {{10}^{ - 4}}\;{\rm{GeV}}} \right)} \right)\\ &= 100\;{\rm{GeV}}\end{align}\)

The total collision energy available, taking into account the annihilation energy is 100 GeV.

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Most popular questions from this chapter

Suppose leptons are created in a reaction. Does this imply the weak force is acting? (for example, consider \(\beta \)decay.)

The decay mode of the negative muon is \({{\rm{\mu }}^{\rm{ - }}} \to {{\rm{e}}^{\rm{ - }}}{\rm{ + }}{{\rm{\bar \nu }}_{\rm{e}}}{\rm{ + }}{{\rm{\nu }}_{\rm{\mu }}}\). (a) Find the energy released in \({\rm{MeV}}\). (b) Verify that charge and lepton family numbers are conserved.

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.

One decay mode for the eta-zero meson is\({{\rm{\eta }}^{\rm{0}}} \to {\rm{\gamma + \gamma }}\).

(a) Find the energy released.

(b) What is the uncertainty in the energy due to the short lifetime?

(c) Write the decay in terms of the constituent quarks.

(d) Verify that baryon number, lepton numbers, and charge are conserved.

(a) Do all particles having strangeness also have at least one strange quark in them?

(b) Do all hadrons with a strange quark also have nonzero strangeness?
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