A beam of charged kaons ( ) is produced with a common laboratory energy

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Particle Physics & Quantum Fields · Particles, interactions and experiment

Particle Physics, Ch Scales, units and the four-momentum

Problem

A beam of charged kaons (

K^+

) is produced with a common laboratory energy

E = 5.000\,\mathrm{GeV}

. The kaon's rest mass is

m_Kc^2 = 493.677\,\mathrm{MeV}

and its mean lifetime, measured in its own rest frame, is

\tau = 1.238\times10^{-8}\,\mathrm{s}

. Every kaon in the beam travels in a straight line at this fixed energy (no energy loss along the flight path), and the number of kaons that have not yet decayed falls off as

N(x) = N_0\,e^{-x/L}

, where

x

is the distance travelled in the laboratory frame and

L

is the mean flight distance in that frame. ((a)) Find

\beta

and

\gamma

of the kaons in the laboratory frame. ((b)) Find the mean flight distance

L

of the kaon beam in the laboratory frame. ((c)) A detector sits

100\,\mathrm{m}

downstream of the production point. What fraction of the beam reaches it undecayed?

Browse the problem library