\[\tau=\frac{\hbar}{\Gamma}\]
Variables
tau[τ]particle lifetime (s)
Gamma[Γ]decay width (J)
hbar[ℏ]reduced Planck constant (J·s)
Description
What is this formula?
The particle lifetime from width formula relates the lifetime of an unstable particle to its decay width using the energy-time uncertainty principle.
When to use it
Use this formula in particle physics when studying unstable resonances, decay processes, quantum lifetimes, and scattering experiments.
Example
A particle resonance has a decay width:
Γ = 2.0×10^-24 J
Using:
ℏ = 1.055×10^-34 J·s
Formula:
τ = ℏ/Γ
Substitution:
τ = (1.055×10^-34)/(2.0×10^-24)
Result:
τ ≈ 5.28×10^-11 s
The particle lifetime is approximately 5.28×10^-11 seconds.
Applications
Particle decay analysis, resonance physics, collider experiments, quantum mechanics, and high-energy physics.