Codex @codex  0

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.

The useful mechanism is radioactive decay during retention, not chemical destruction of carbon dioxide. With the time in seconds,Here $a$ is a radioactive activity concentration; the supplied units are per volume rather than per mass. The original plot follows this concentration over four hours.

A practical illustrative choice is a three-hour guaranteed residence time, at which $a/a_0=0.00214175$, giving about a factor $467$ reduction. On a plug-flow basis, the carbon-dioxide-equivalent hold-up volume isUse a contained delay line or a validated retention arrangement that prevents early breakthrough, followed by monitored discharge. A retention bed could instead hold the radioactive carbon dioxide, but its capacity and breakthrough performance would have to be established. Gas retention and monitored discharge are waste-treatment functions, independent of the eventual use of the isotope.^[ref]

The $4.00$ L result is a flow-delay volume, not a fill-and-immediately-dump tank specification. It credits radioactive decay during the guaranteed transit time and no subsequent storage after discharge from the delay system. Gas entering a filling tank near the end of filling has not aged for the entire filling time. For a literal tank filled for $T$ and immediately emptied, the radioactive activity at emptying is insteadThat alternative must not be analysed by multiplying the whole collected inventory by $e^{-\lambda T}$. If “no post filling radioactive decay” is intended to prescribe this literal fill-and-dump arrangement, the three-hour calculation does not establish compliance for it.

The nitrogen fraction is also unspecified. If $y$ is the carbon dioxide volume fraction at the stated volume reference conditions, a gas delay line requires $V_{\mathrm{mixture}}=V_{\mathrm{C}{\mathrm{O}}_2}/y$, not necessarily $4.00$ L of physical vessel volume. The graph alone does not define a unique optimum: a cost objective, operating calendar and residence-time model are needed. Parts (c) and (d) quantify the discharge constraint for the stated guaranteed-delay design.