3.8.1.3
Activity is the number of decays per second: $A = \lambdaN$
Radioactive Decay & Half-Life — AQA A-Level Physics
Key Definition
Activity (A) — The average number of nuclei that decay per unit time. Measured in becquerels (Bq), where 1 Bq = 1 decay per second.
Key Definition
Decay constant (λ) — The probability that an individual nucleus will decay per unit of time. Unit: s⁻¹.
$$A = \lambda N$$
- $A$: activityThe number of nuclear decays per unit time. Measured in becquerels (Bq), where 1 Bq = 1 decay per second. (Bq)
- $λ$: decay constantThe probability of decay of a nucleus per unit time. Measured in s⁻¹. (s⁻¹)
- $N$: number of undecayed nuclei remaining
- The greater the decay constantThe probability of decay of a nucleus per unit time. Measured in s⁻¹., the greater the activityThe number of nuclear decays per unit time. Measured in becquerels (Bq), where 1 Bq = 1 decay per second. for a given number of nuclei.
- ActivityThe number of nuclear decays per unit time. Measured in becquerels (Bq), where 1 Bq = 1 decay per second. depends on how many undecayed nuclei remain — as N decreases, A decreases.
- The minus sign in $A = -\Delta N/\Delta t$ indicates that the number of undecayed nuclei decreases over time.
Worked Example
A sample of radium-226 containing 3.2 × 10²² atoms has an activity of 12 Ci. Given that 1 Ci = 3.7 × 10¹⁰ Bq, calculate the decay constantThe probability of decay of a nucleus per unit time. Measured in s⁻¹..
Show Solution
1
Convert activity to Bq
$$A = 12 \times 3.7 \times 10^{10} = 4.44 \times 10^{11} \text{ Bq}$$
2
Use A = λN
$$\lambda = \frac{A}{N} = \frac{4.44 \times 10^{11}}{3.2 \times 10^{22}} = 1.4 \times 10^{-11} \text{ s}^{-1}$$
Answer
$\lambda = 1.4 \times 10^{-11}$ s⁻¹