Radioactive activity ($A=\lambda N$)

With $n$ parent atomic nuclei present, the conditional expected number of transformations in a short interval is approximately $\lambda n\Delta t$. The corresponding radioactive activity is $A=\lambda n$. Averaging over the finite-population radioactive decay model gives $\overline{A}(t)=\lambda \overline{N}(t)$. Its unit is the becquerel.^[ref]

For a finite counting interval, depletion matters. Suppose each transformation is recorded independently with detection efficiency $\epsilon$, with at most one count per transformation and no background. The expected value of the count between $t$ and $t+\Delta t$ isOnly when $\lambda \Delta t\ll 1$ does this become approximately $\epsilon \overline{A}(t)\Delta t$. A count rate therefore needs a detector model before it can be interpreted as the source's radioactive activity.

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.

radioactive activity per volume, in $\mathrm{Bq}{\mathrm{m}}^{-3}$. This differs from mass-specific radioactive activity, usually expressed per kilogram.

The becquerel, symbol $\mathrm{Bq}$, is the SI unit of radioactive activity, with $1\mathrm{Bq}=1{\mathrm{s}}^{-1}$. An radioactive activity of one becquerel means one expected nuclear transformation per second under the stated conditions, not a guarantee of one event in every individual second.

Measured count rate need not equal radioactive activity. A particle detector registers only some decays because of geometry and detection efficiency, and one transformation can emit several particles or none detectable by that instrument. Activity also differs from deposited energy or absorbed dose: those depend on the emitted particles, their energies and where their interactions occur.

The probability that an event of a specified kind produces a registered count in a specified arrangement. For a radiation detector, geometry, intervening material and the detector response can all affect detection efficiency.