\[P=1-e^{-t/\tau}\]
Variables
Pdecay probability
telapsed time (s)
tau[τ]mean lifetime (s)
Description
What is this formula?
The decay probability formula calculates the probability that an unstable particle has decayed after a given elapsed time. It follows the exponential decay law used in particle and nuclear physics.
When to use it
Use this formula when studying radioactive decay, unstable particles, detector timing, and statistical decay processes.
Example
An unstable particle has a mean lifetime of:
tau = 2.0×10^-6 s
Calculate the decay probability after:
t = 5.0×10^-6 s
Formula:
P = 1 - e^(-t/tau)
Substitution:
P = 1 - e^(-(5.0×10^-6)/(2.0×10^-6))
Result:
P ≈ 0.918
There is approximately a 91.8% probability that the particle has decayed.
Applications
Particle physics, radioactive decay analysis, detector systems, timing electronics, and nuclear physics experiments.