\[L=\gamma v\tau\]
Variables
Lrelativistic decay length (m)
gamma[γ]Lorentz factor
vparticle velocity (m/s)
tau[τ]proper lifetime (s)
Description
What is this formula?
The relativistic decay length formula calculates the average distance traveled by an unstable particle before decaying when relativistic effects are significant.
When to use it
Use this formula in high-energy physics, accelerator experiments, cosmic ray studies, and relativistic particle transport calculations.
Example
A relativistic particle travels with:
gamma = 12
v = 2.9×10^8 m/s
tau = 2.5×10^-8 s
Formula:
L = gamma*v*tau
Substitution:
L = 12*(2.9×10^8)*(2.5×10^-8)
Result:
L ≈ 87 m
The particle travels an average distance of approximately 87 meters before decaying.
Applications
Particle accelerators, detector design, muon decay analysis, relativistic transport studies, and experimental particle physics.