Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

(a) Calculate the relativistic quantity \(\gamma {\rm{ = }}\frac{{\rm{1}}}{{\sqrt {{\rm{1 - }}{{\rm{v}}^{\rm{2}}}{\rm{/}}{{\rm{c}}^{\rm{2}}}} }}\) for \({\rm{1}}{\rm{.00 - TeV}}\) protons produced at Fermilab.

(b) If such a proton created a \({\pi ^{\rm{ + }}}\) having the same speed, how long would its life be in the laboratory?

(c) How far could it travel in this time?

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 neutrinoโ€™s mass. (Hint: You may need to use a series expansion to find \({\rm{v}}\) for the neutrino, since it \(\gamma \) is so large.)

Discuss the similarities and differences between the photon and the Z0in terms of particle properties, including forces felt.

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

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

(c) Why is this energy greater than the protonโ€™s total mass (converted to energy)?

There are particles called \({\rm{D}}\)-mesons. One of them is the \({{\rm{D}}^{\rm{ + }}}\) 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 \({\rm{ + 1}}\). What is its quark configuration?

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free