E.3.12—Half-life changes

Use integer half-lives

If activity changes from $A_0$ to $A$, use $A/A_0=(1/2)^n$ to find the number of half-lives $n$. For example, a fall to one-eighth means three half-lives.

Worked example — integer half-lives

A net count rate falls from $640\,\mathrm{s^{-1}}$ to $80\,\mathrm{s^{-1}}$ in 18 h. Since $80/640=1/8=(1/2)^3$, three half-lives elapsed. Therefore $T_{1/2}=18/3=6.0\,\mathrm{h}$.

Find the half-life

Once $n$ is known, divide the elapsed time by $n$: $T_{1/2}=t/n$. This is often quicker and clearer than starting with the exponential form.

Check the direction

A decay interval must reduce activity or count rate. If the calculated half-life or number of half-lives implies growth, revisit the ratio.

Common trap

Do not call a drop to one-eighth “one half-life”; half-life is the time for one factor of one-half.