Massic activity
= Massic activity
{title2=$a_m=A/m$}
<Massic activity> is a sample's <radioactive activity> divided by its <mass>:
$$
a_m=\frac{A}{m}.
$$
Its <SI> unit is the <becquerel> per <kilogram>, $\mathrm{Bq\,kg^{-1}}$. State both the material included in the denominator and the time to which the activity refers. For a solution, the mass of the complete sample is different from the mass of its radioactive constituent.<Massic Activity Ratios of the NBS NIST Tritiated-Water Standards Issued Between 1954 and 1999 by L. L. Lucas>[Abstract, explicit definition as sample activity divided by sample mass]{ref}
For an own bookkeeping example, suppose a sample has total activity $A=60\,\mathrm{Bq}$ and total mass $m=0.020\,\mathrm{kg}$ at a specified instant. Then
$$
a_m=\frac{60}{0.020}=3000\,\mathrm{Bq\,kg^{-1}}.
$$
Imagine adding nonradioactive material so that the total mass becomes $0.040\,\mathrm{kg}$, with no loss of activity and no relevant elapsed decay time. The total activity remains $60\,\mathrm{Bq}$, but
$$
a_m=\frac{60}{0.040}=1500\,\mathrm{Bq\,kg^{-1}}.
$$
A lower massic activity therefore does not by itself demonstrate radioactive decay or loss of radioactive atoms: the denominator can change.
Time introduces a separate effect. For a fixed sample mass and a single decaying constituent with <radioactive decay constant> $\lambda$, use the usual mean exponential law:
$$
A(t)=A(0)e^{-\lambda t}
\quad\Longrightarrow\quad
a_m(t)=a_m(0)e^{-\lambda t}.
$$
After one <half-life>, the massic activity halves under those assumptions. Comparing standards requires either a common reference time or the appropriate decay correction. Additional radioactive constituents, production of daughter activity or changing sample mass require a correspondingly different model.
The quantity also supports experimental cross-checks. In a 2000 study, <L. L. Lucas> compared massic-activity ratios of available NBS/NIST water standards containing <tritium>, issued between 1954 and 1999. <Liquid scintillation counting> supplied measured ratios; where the records allowed it, <gravimetric dilution> supplied independently calculated ratios. The paper reports agreement within the stated <measurement uncertainties>.<Massic Activity Ratios of the NBS NIST Tritiated-Water Standards Issued Between 1954 and 1999 by L. L. Lucas>[Abstract, available standards, liquid-scintillation comparison and gravimetric dilution factors]{ref}
This compares two kinds of evidence: radioactive counting with its detector response, and mass-based preparation records. A measured count rate still needs a <detection efficiency> and measurement model before it becomes an activity estimate. Dividing a detector's raw counts by sample mass alone is not the definition of <massic activity>. Also distinguish <radioactive activity concentration>, which uses volume rather than mass in the denominator.