SCIENCE · INVESTIGATE AND EXPLAIN

Distinguish activity from remaining inventory and dose

Calculate activity from survivor number and half-life and explain why activity alone does not determine dose.

Learning outcome: Calculate activity from survivor number and half-life and explain why activity alone does not determine dose.

Starting recap

Activity is a decay rate measured in becquerels, one decay per second.

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Try

Two virtual ensembles each have 800 expected parents remaining, but half-lives 20 s and 40 s.

Open the experiment

Predict

Must equal remaining parent counts imply equal activities?

Your prediction and reason

Experiment

At one half-life compare T 20 s and 40 s. Then hold T 20 s and compare zero, one and two half-lives.

Compare survivor number and activity

Worked teaching model · synthetic values · Original ensemble of 1600 independent identical parents, no replenishment or daughter feedback. Smooth values are expectations, not integer observations or a clock for one nucleus. Activity is decays per second, not dose.

Elapsed quarter-half-lives: 4 quarters Half-life: 20 s

Reset keeps your prediction, captures and practice history.

Quantity	Calculated value	Unit
Expected parents remaining	800.0000	expected nuclei
Expected parents transformed	800.0000	expected nuclei

800.000 expected survivors after 1 half-lives.

Elapsed time 20 s; activity 27.7259 Bq. Changing half-life at fixed half-life count preserves survivors but changes time and activity. No dose or safety limit follows.

Model boundary: Original ensemble of 1600 independent identical parents, no replenishment or daughter feedback. Smooth values are expectations, not integer observations or a clock for one nucleus. Activity is decays per second, not dose.

All investigations are virtual. Do not obtain radioactive sources, expose eyes to bright beams, or build high-voltage apparatus. Notebook captures preserve selected recipes, not physical measurements.

800.000 expected survivors after 1 half-lives.

Elapsed time 20 s; activity 27.7259 Bq. Changing half-life at fixed half-life count preserves survivors but changes time and activity. No dose or safety limit follows.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Count and rate answer different questions

Inventory asks how many parent nuclei remain. Activity asks how rapidly those parents transform at the selected instant. Write the decay constant as λd=ln 2/T, using a subscript to avoid confusing it with photon wavelength. Activity is A=λdN. If T is in seconds, A is in inverse seconds, reported as becquerels.

At one 20 s half-life, the model has 800 expected parents. Activity is(ln 2/20)×800≈27.73 Bq. At one 40 s half-life, the same 800 remain, but activity is 13.86 Bq. The selected elapsed times are also different:20 s and 40 s. Always identify what a comparison holds fixed.

Compare at the same clock time

The browser’s first control is a half-life fraction, not absolute time. To compare both samples after 20 s, choose one half-life for T=20 s but half a half-life for T=40 s. The second sample then has approximately 1131.37 survivors and activity 19.61 Bq. It retains more parents but has a lower instantaneous activity. An apparent contradiction disappears once the independent variable is made explicit.

Detector counts require calibration

A detector may record only a fraction of decays and may also record background. In a simplified original example, an observed 120 counts/s with 20 counts/s background and 50% efficiency suggests a source rate of(120−20)/0.50=200 Bq, provided geometry and emission assumptions justify that efficiency. A count is not automatically one source decay.

Transfer: compare two known inventories

Sample A has 400 parents and T=10 s; sample B has 800 parents and T=40 s. Their expected activities are 27.73 Bq and 13.86 Bq respectively. More parents does not guarantee greater activity when decay constants differ.

Do not turn a rate into a safety claim

Energy per decay, radiation type, geometry, exposure duration, absorption and the material receiving energy all affect absorbed dose and biological consequences. The current model does not calculate them. A becquerel is not a gray or a sievert, and no conversion can be made without additional physical information. The lesson supplies synthetic numbers for reasoning, not a radiological survey or advice for handling materials.

Source and authorship

Reference for the physical relationship. Source checked 30 October 2026. The explanations, numerical cases, questions and diagrams here are original; reference material is not copied. Exact h,c,e follow NIST SI definitions.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Show A=(ln 2/T)N with seconds. Explain why a larger activity is not by itself a complete measure of biological effect.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

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Previous: Predict an ensemble without assigning a lifetime to one nucleus Next: Account for rest mass and released energy

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