Learning Materials
Features
Discover
Chapter 33: Q11CQ (page 1210)
Why does the \({\eta ^0}\) meson have such a short lifetime compared to most other mesons?
As, the \({\eta ^0}\) meson consists of quark-antiquark pairs of the same flavour, its lifetime is short.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Plans for an accelerator that produces a secondary beam of \({\rm{K}}\)-mesons to scatter from nuclei, for the purpose of studying the strong force, call for them to have a kinetic energy of \({\rm{500 MeV}}\).
(a) What would the relativistic quantity \(\gamma {\rm{ = }}\frac{{\rm{1}}}{{\sqrt {{\rm{1 - }}{{{{\rm{\nu }}^{\rm{2}}}} \mathord{\left/{\vphantom {{{{\rm{\nu }}^{\rm{2}}}} {{{\rm{c}}^{\rm{2}}}}}} \right. \\} {{{\rm{c}}^{\rm{2}}}}}} }}\) be for these particles?
(b) How long would their average lifetime be in the laboratory?
(c) How far could they travel in this time?
The decay mode of the positive tau is\({{\bf{\tau }}^ + } \to {\rm{ }}{{\bf{\mu }}^ + }{\rm{ }} + {\rm{ }}{{\bf{\nu }}_{\bf{\mu }}}{\rm{ }} + {\rm{ }}{{\bf{\bar \nu }}_{\bf{\tau }}}\).
(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 \(\tau {\rm{ }} - \)due to its short lifetime?
(b) Is the uncertainty in this energy greater than or less than the uncertainty in the mass of the tau neutrino? Discuss the source of the uncertainty.
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.
The primary decay mode for the negative pion is \[{\pi ^ - } \to {\mu ^ - } + {\bar \nu _\mu }\]. What is the energy release in MeV in this decay?
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App