---
title: "Activity, Half-Life and Radioactive Dating"
description: "Activity is the decay constant times the number of nuclei, so it falls on the same curve as the nuclei do, and the half-life is ln 2 divided by the decay constant. Comparing the activity left with the"
canonical: https://lightmysky.com/learn/science/activity-half-life-and-radioactive-dating-mt_LvZw4h5wlu
source: https://lightmysky.com/learn/science/activity-half-life-and-radioactive-dating-mt_LvZw4h5wlu.md
retrieved: 2026-09-12
---

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# Activity, Half-Life and Radioactive Dating

Activity is the decay constant times the number of nuclei, so it falls on the same curve as the nuclei do, and the half-life is ln 2 divided by the decay constant. Comparing the activity left with the activity at the start dates a sample.

Subject: Science · Area: Matter & Materials · Ages 17 to 18
Page: https://lightmysky.com/learn/science/activity-half-life-and-radioactive-dating-mt_LvZw4h5wlu

## Ready when they can

- Converts between half-life and decay constant in both directions
- Calculates activity in becquerels from the number of nuclei present
- Dates a sample from a measured carbon-14 activity and names one assumption the method makes

## Lesson: Counting decays to tell the time

Activity tells you how strong a sample really is right now, since it counts the decays per second. It equals the decay constant times the nuclei present, and one becquerel means one decay each second. As nuclei dwindle, activity slides down the same exponential curve, since fewer nuclei mean fewer decays.

**Example.** Try the activity rule on clean numbers. A sample holds 4000 nuclei with lambda 0.5 per second. Multiply: 0.5 times 4000 gives 2000 decays per second, so the activity is 2000 Bq. Halve the nuclei and the activity halves too.

Carbon-14 dating turns this curve into a clock. Living wood keeps a steady share of carbon-14, which has a half-life of 5730 years. Charcoal with half the living activity died one half-life ago, so 5730 years. With a quarter, two half-lives passed, so 11460 years. The Shroud of Turin keeps 92 percent, giving about 690 years.

Name the assumption before you trust a date. The method needs the air level steady while the organism lived, and no carbon entering or leaving since death. Convert either way with lambda equals 0.693 over half-life, and check whether contamination could fake the ratio.

**Recap.** Activity tracks the nuclei downward, and the leftover fraction of carbon-14 converts straight into years.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Half-Life and Activity](https://lightmysky.com/learn/science/half-life-and-activity-mt_S5snTqUjyi)
- [The Decay Constant and the Exponential Decay Law](https://lightmysky.com/learn/science/the-decay-constant-and-the-exponential-decay-law-mt_VIydSAys1W)