Beta Phase: Square45 is currently in beta testing. Expect some features or content to be incomplete or missing.

Half-Life

The time it takes for half of the radioactive nuclei in a sample to decay, a fundamental parameter in radioactive decay processes.

📜

The statement of the theorem

Let

N(t)

be the number of radioactive nuclei at time

t

, and

\lambda

be the decay constant. The decay follows the differential equation

\frac{dN}{dt} = -\lambda N

. The half-life

T_{1/2}

is defined implicitly by the condition

N(T_{1/2}) = \frac{1}{2} N(0)

, yielding:\n

T_{1/2} = \frac{\ln(2)}{\lambda}