What are the units of a half-life?

Jul 13, 2016

The units of half-life are time.

Explanation:

The units of half-life are time. The half-life is the length of time that it takes for half of an initial sample to undergo a change. Usually this is the radio-active decay of a specific atomic weight of an element. For example, the half-life of Uranium-238 is 4.46 billion years.

The formula for half-life which gives the number of remaining atoms after a time, $t$, and starting with $N \left(0\right)$ atoms in the sample:

$N \left(t\right) = N \left(0\right) {\left(\frac{1}{2}\right)}^{\frac{t}{t} _ \left(1 / 2\right)}$

where ${t}_{1 / 2}$ is the half-life in units of time. This is clear from the formula, since the power must be unitless, so the units of half-life must cancel with the units of the time, $t$.