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Gravimetric dilution determines a dilution from measured masses. A measured amount of a stock solution is combined with material containing none of the quantity being diluted. For a closed transfer and a homogeneous mixture, the conserved amount divided by the final mass determines the new mass-based concentration.

Let $m_s$ be the stock's net mass, $m_d$ the added net mass, and $M=m_s+m_d$. Define the stock fraction $f$ and the gravimetric dilution factor $F$ byIf the stock has solute mass fraction $w_s$, thenFor stipulated $m_s=2.000\mathrm{g}$, $m_d=18.000\mathrm{g}$ and $w_s=0.2000$, the final mass is $20.000\mathrm{g}$, $F=10$, and $\boxed{w_f=0.02000}$: 2% by mass. The solute mass is $0.4000\mathrm{g}$ before and after dilution. The net masses exclude their containers. This mass basis does not require an assumption that liquid volumes add.

The uncertainty of a gravimetric dilution depends on which readings share errors. For independently evaluated inputs $w_s,m_s,m_d$, first-order propagation of uncertainty givesHere $u$ denotes standard uncertainty. The sensitivity factors follow from the partial derivatives $\partial f/\partial m_s=m_d/M^2$ and $\partial f/\partial m_d=-m_s/M^2$. With a chosen independent $u(m_s)=u(m_d)=0.001\mathrm{g}$ at the example's nominal masses, the relative mass-ratio contribution is approximately 0.0453%. Adding an independent 0.5% relative stock-value contribution in quadrature gives approximately 0.502%. These are illustrative inputs, rather than a balance specification.^[ref]

If input errors have covariance, their cross terms must be retained. A useful exact check isA common multiplicative mass-scale factor therefore cancels from $f$. Counting it as two independent contributions would lose that correlation. Container subtraction, transfer losses and changes in composition require their own assessment; this cancellation establishes only the common-scale property.

For massic activity, the same conservation argument applies after expressing all activities at a common reference time. A 2000 NIST study compared massic activity ratios inferred from gravimetric dilution with independent liquid scintillation counting. Their agreement within reported uncertainties provided an experimental check on transferring standards through mass ratios.^[ref]

Liquid scintillation counting measures radiation through light produced in a liquid scintillator containing the radioactive sample. Energy deposited in the medium leads to optical emission, which photomultipliers detect as pulses. The apparatus is a scintillation counter, but the measured pulse rate still needs a model connecting it to radioactive activity.^[ref]

In an idealized one-count-per-decay model with background subtracted and other corrections negligible,where $A$ is radioactive activity and $\epsilon$ is detection efficiency. A hypothetical net rate of $100{\mathrm{s}}^{-1}$ with $\epsilon =0.40$ corresponds to $A=250\mathrm{Bq}$. At the same activity, an efficiency of $0.20$ would produce only $50{\mathrm{s}}^{-1}$. A smaller count rate need not mean that fewer decays occur.

A motivating measurement example is L. L. Lucas's comparison of tritium-containing water standards. Liquid scintillation counting supplied massic activity ratios that could be compared with independently recorded mass-based dilutions. Agreement within stated measurement uncertainties supports consistency of the standards; it does not turn the counting apparatus into an uncertainty-free activity meter.^[ref]

L. L. Lucas authored a 2000 comparison of water standards containing tritium, using liquid scintillation counting to measure their massic activity ratios. Massic activity is radioactive activity divided by sample mass. The work compared these measured ratios with ratios obtained from recorded mass-based dilutions, finding agreement within the stated measurement uncertainties.^[ref]

The comparison illustrates an important measurement calibration principle: independently obtained ratios can test consistency without making every source of error disappear. Agreement between counting and dilution supports the relationship between the standards. It does not imply zero measurement uncertainty, nor does it by itself establish an absolute radioactive activity scale. The study's contribution was a quantitative connection between reference samples, rather than simply a count from one detector.^[ref]

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.

M. P. Unterweger coauthored a 2000 study of measurement calibration for water standards containing tritium. The paper combined measurements using a proportional counter with liquid scintillation counting comparisons. It also followed massic activity data spanning 38 years to estimate a tritium half-life of $4504\pm 9$ days, with the uncertainty specified as one standard deviation.^[ref]

The long time record makes a useful distinction visible. A reference sample's radioactive activity changes through radioactive decay even when its chemical identity is unchanged. In an ideal closed sample with constant half-life $T_{1/2}$,Measurements made at different times must therefore be related to a common time before differences can be interpreted as inconsistent standards. A half-life determination and a detector comparison address related but distinct parts of that problem.