Explore BrainMass
Share

# Pi-Meson Decay

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

I am confused as to how to apply the 10% accuracy in the attached problem. Also, I am not sure how to set up the problem just to get the minimum value.

https://brainmass.com/physics/decay-paths/pi-meson-decay-139582

#### Solution Preview

The explanations are written in the attached pdf file.

The web pages referenced there are
http://en.wikipedia.org/wiki/Pion
http://en.wikipedia.org/wiki/Time_dilation
http://en.wikipedia.org/wiki/Lorentz_transformation

Here is the plain TEX source:

centerline{bf \$pi^0to gammagamma\$ decay}

As the \$pi^0\$ rest mass is \$135~MeV/c^2\$ (see e.g. http://en.wikipedia.org/wiki/Pion),
a \$pi^0\$ with momentum \$135~GeV/c\$ has \$gamma\$-factor
\$\$
gamma = {1oversqrt{1-beta^2}} approx 1000,
eqno(1.1)
\$\$
where \$beta = v/c\$, \$vapprox c\$ is its velocity, and \$capprox 3times 10^8~m/s\$ is the
speed of light.
Given rest-frame mean life \$tau_0 = 8.5times 10^{-17}~s\$,
the Lorentz time dilation results in mean decay path of
\$\$
lambda = cgammatau_0
eqno(1.2)
\$\$
(see e.g. ...

#### Solution Summary

I am confused as to how to apply the 10% accuracy in the attached problem. Also, I am not sure how to set up the problem just to get the minimum value.

\$2.19