Editing Specific activity (section)

===Calculation of half-life from specific activity===
Experimentally measured specific activity can be used to calculate the [[half-life]] of a radionuclide.

Where decay constant ''λ'' is related to specific radioactivity ''a'' by the following equation:

: <math>\lambda = \frac{a \times M}{N_\text{A}}.</math>

Therefore, the half-life can also be described by

: <math>T_{1/2} = \frac{N_\text{A} \ln 2}{a \times M}.</math>

==== Example: half-life of Rb-87 ====
One gram of [[Isotopes of rubidium|rubidium-87]] and a radioactivity count rate that, after taking [[solid angle]] effects into account, is consistent with a decay rate of 3200 decays per second corresponds to a specific activity of {{val|3.2|e=6|u=Bq/kg}}. Rubidium [[atomic mass]] is 87&nbsp;g/mol, so one gram is 1/87 of a mole. Plugging in the numbers:

: <math>
 T_{1/2} =
 \frac{N_\text{A} \times \ln 2}{a \times M} \approx \frac{6.022 \times 10^{23}\text{ mol}^{-1} \times 0.693}
      {3200\text{ s}^{-1}{\cdot}\text{g}^{-1} \times 87\text{ g/mol}} \approx
 1.5 \times 10^{18}\text{ s} \approx 47\text{ billion years}.
</math>