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The gravimetric dilution factor is the ratio of final mixture mass to the stock mass used in a gravimetric dilution:Here $m_d$ is added diluent mass and $f$ is the retained stock mass fraction. For a diluent containing none of the component being measured, mass conservation gives final component mass fraction $w_f=w_s/F$. This mass-based relation avoids assuming that liquid volumes are additive. Its uncertainty follows from the same input masses and their covariance as the uncertainty of a gravimetric dilution.^[ref]

For an original two-step example, combine $2.000\mathrm{g}$ of stock with $18.000\mathrm{g}$ of diluent, giving $F_1=10$. After complete mixing, transfer $1.000\mathrm{g}$ of that mixture and add $4.000\mathrm{g}$ of diluent, giving $F_2=5$. The combined gravimetric dilution factor isIf the original stock has component mass fraction $0.2000$, the first mixture has $0.02000$ and the final mixture $0.004000$. The transferred gram contains $0.02000\mathrm{g}$ of the component; dividing by the final $5.000\mathrm{g}$ checks the result. This calculation requires a representative, homogeneous transferred portion and no component loss.

State whether a dilution number denotes $F$ or its reciprocal $f$: here a tenfold dilution means $F=10$ and $f=0.1$, not that ten parts of diluent were added per part of stock. The latter recipe gives $F=11$.

Massic activity is a sample's radioactive activity divided by its mass:Its SI unit is the becquerel per kilogram, $\mathrm{Bq}\mathrm{k}{\mathrm{g}}^{-1}$. 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.^[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. ThenImagine 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 $60\mathrm{Bq}$, butA 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: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.^[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.