Decay constant: half-life

The half-life is related to the decay constant with a simple equation.

When the number of atoms left in a sample, N, is half the original, No....

Taking logs to the base e of both sides gives....

Since log to the base e of one half, is equal to - 0.69, we have at once....

If a half-life is given as 20 seconds, the decay constant is 0.0345 s-1

If a decay constant is given as 0.45 years-1, the half-life is 1.5 years.