quantity

lifetime

The average time a particle exists before decaying.
18 related articles · 1 formulas

Description

Lifetime, in particle physics, is the average time a particle exists before it decays into other particles. It is a fundamental property of unstable particles, ranging from fractions of a second (like the top quark, ~5×10⁻²⁵ s) to billions of years (like the neutron in a nucleus, effectively stable). The lifetime is intimately connected to the particle's mass and the strength of the interactions that cause its decay. For example, particles decaying via the weak force have longer lifetimes than those decaying via the strong or electromagnetic forces.

History

The concept of particle lifetime emerged in the early 20th century with the study of radioactivity. Ernest Rutherford and Frederick Soddy formulated the exponential decay law in 1902, and the quantum mechanical understanding was developed in the 1920s-30s.

How it works

The lifetime is defined by the exponential decay law: if you have a large population of identical particles, the number remaining after time t is N(t) = N₀ e^(-t/τ), where τ is the mean lifetime. This is not a deterministic process — you cannot predict when a single particle will decay, only the probability distribution. The lifetime is related to the decay width Γ (the energy uncertainty of the particle) by the Heisenberg uncertainty principle: τ = ħ/Γ. Measuring lifetimes often involves creating many particles, tracking their decays in detectors, and fitting the observed time distribution.

In practice

Lifetime measurements are crucial for identifying new particles at colliders like the LHC, for understanding the early universe's nucleosynthesis (e.g., neutron lifetime), and for medical imaging techniques like PET scans that rely on positron annihilation lifetimes.

Fun fact

The muon, a heavier cousin of the electron, has a lifetime of about 2.2 microseconds — long enough to travel hundreds of meters at near-light speed, which is why muons created in the atmosphere reach the ground despite their short lifetime.

Concept graph →

Formulas

$$\tau = \frac{1}{\lambda}$$
The lifetime is the reciprocal of the decay rate constant.
What is in the formula
\tauvariablelifetime — lifetime second
\lambdavariabledecay rate constant — decay rate per second

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