Activity as Decays per Second

Introduction

A radioactive source can contain many unstable nuclei, but its activity tells how quickly they transform, not simply how many are present. One becquerel (Bq) means one nuclear decay per second. This simple definition becomes useful only when we separate activity from the radiation a detector counts and from energy absorbed by matter. Those quantities respond differently to geometry, shielding and radiation type.

Core explanation

Activity A is the expected number of decays per unit time in a source. The SI unit is the becquerel: 1 Bq = 1 decay s⁻¹. If a sample averages 250 decays in each second over an appropriate observation interval, its activity is 250 Bq. The statement is statistical. A counter might record 247 decays in one second and 263 in the next even if the underlying average rate is steady, because individual decay times vary.

Do not confuse the activity symbol A with mass number A in nuclide notation. Both are traditional symbols used in different contexts. Mass number is a dimensionless integer written at the upper left of a nuclide symbol; activity is a measured rate with units Bq. Writing the units and context prevents ambiguity. In equations for exponential decay, activity is often related to the number N of undecayed nuclei by A = λN, where λ is the decay constant. More undecayed nuclei of one nuclide generally means more decays per second, while the same number of atoms of a longer-lived nuclide can have much lower activity.

A detector records a count rate, often counts per second. It usually detects only some emissions from the source: some travel away, some are absorbed before reaching it, and some pass through the detector without registering. Detector efficiency varies with radiation type and energy. Background radiation also contributes counts. Therefore count rate is not automatically equal to source activity. If a detector records 80 counts per second in the presence of a source and 5 counts per second as background under comparable conditions, the source's net detected count rate is about 75 counts per second, not necessarily 75 Bq.

Absorbed dose asks a different question: how much radiation energy is deposited per unit mass of material. Its SI unit is the gray (Gy), equal to one joule per kilogram. Activity alone does not determine dose because emissions have different energies and may or may not reach the material. Equivalent or effective dose uses sieverts in radiation-protection contexts and accounts for additional biological weighting. A student should not convert Bq directly to Gy or Sv without an exposure model and more information.

The relation between activity and sample mass also requires isotope identity. A small quantity of a short-lived isotope can have high activity, while a larger quantity of a long-lived isotope can have lower activity. Similarly, two samples with the same activity can give different external detector readings or absorbed doses if their radiation types, energies, packaging and distances differ. “More radioactive” should therefore be made precise: does it mean more decays per second, more detected counts or more exposure in a particular setup?

Activity changes as unstable nuclei decay. For a single isotope with no replenishment, the expected activity decreases with the same half-life as its undecayed population because A = λN and λ stays fixed for that nuclide. A chain can be more complicated because daughters may themselves be radioactive and may be produced while they decay. A total source activity can therefore include contributions from multiple nuclides.

Measurement intervals matter. Counting for longer often gives a more reliable estimate of an average rate because random fluctuations have a smaller relative effect. It does not make individual decay times predictable. The detector's background and efficiency must still be considered when using its count rate to infer the source activity.

Step-by-step reasoning

1. Identify whether a reported number refers to source decays, detected counts or absorbed energy. 2. Convert a stated number of decays over a time interval to decays per second for activity. 3. Use Bq only for activity and counts s⁻¹ for a detector count rate. 4. Subtract a comparable background count rate to estimate net detected counts. 5. Avoid inferring dose from activity without radiation-energy and exposure information.

Visual explanation

Draw a box labelled “source: 100 decays/s” with arrows in many directions. Place a shield and a detector along one direction, and show only some arrows reaching and registering in the detector. A separate tissue box receives different arrows. Label the three quantities: source activity in Bq, detector count rate in counts/s and deposited energy per mass in Gy.

Real-world analogy

A stadium may release a fixed average number of people each minute, but a doorway counter on one street sees only those who take that route. The release rate resembles activity and the doorway rate resembles detected counts. The analogy does not describe radiation energy or absorbed dose, which require separate measurement.

Real-world example

A laboratory counter can measure the gross rate near a source and then the background rate with the source removed, keeping geometry and counting time comparable. Subtracting the rates gives an estimate of source-related detector counts. Calibration and efficiency are still needed before converting that result into a source activity.

Why?

Why can a detector show fewer counts per second than the source's becquerel value? Radiation spreads in different directions, can be absorbed before reaching the detector and may fail to trigger it even when it arrives. The detector observes only a subset of decay emissions, while Bq counts the nuclear transformations in the source.

Common misconception

“A 100-Bq source gives a dose of 100 units.” Bq describes decays per second, not absorbed energy per mass or biological effect. No direct numerical dose follows without radiation type, energy, geometry, exposure duration and absorption details.

Worked example

During a 40-second interval, a source is estimated to undergo 12,000 decays. Its average activity over that interval is 12,000 ÷ 40 = 300 decays per second = 300 Bq. A detector in one position records 2,400 total counts during the same 40 seconds, giving 60 counts/s. A separate background measurement gives 4 counts/s, so the estimated net detected rate is 56 counts/s. The 300-Bq source activity and 56-count/s net detector rate can both be correct; the latter reflects detector geometry, efficiency and absorption.

Quick check

1. What does a source activity of 2 kBq mean? Answer: It means an average of 2,000 nuclear decays per second in that source.

Exam focus

State 1 Bq = 1 decay per second and keep activity separate from count rate and dose. Include time units in calculations. If background is provided, subtract it from gross detector counts only when the measurement conditions are comparable.

Advanced insight

For a pure radioactive nuclide, activity A = λN links the microscopic probability of decay to a macroscopic rate. The decay constant λ has units s⁻¹. Relative counting uncertainty from random events decreases as more counts are accumulated, roughly in proportion to one over the square root of the count total under a simple Poisson model.

Summary

Activity measures expected nuclear decays per second and is expressed in becquerels. A detector's count rate includes efficiency, geometry and background effects, while absorbed dose concerns deposited energy per mass. These three quantities cannot be substituted for one another without additional information.

Practice questions

1. A source undergoes 9,000 decays in 30 seconds on average. What is its activity? Answer: 9,000 ÷ 30 = 300 decays/s, so the activity is 300 Bq. 2. A detector reads 48 counts/s with a source and 6 counts/s without it. What is the net detected rate? Answer: 48 − 6 = 42 counts/s under comparable measurement conditions; this is not automatically 42 Bq. 3. Can two sources with equal Bq values give different absorbed doses? Answer: Yes. Radiation type and energy, distance, shielding and absorption can differ even when decay rates match.