Activity

This lesson covers: 

1. Understanding radioactive decay rates and the decay constant
2. Defining and explaining activity in terms of decay rate
3. Using equations to relate decay rate, number of nuclei, and time
4. Calculating decay constants from activity measurements

Decay rates and the decay constant

Various radioactive isotopes decay at differing rates by emitting radiation. The decay constant, denoted as (λ), is a measure that indicates the likelihood of a radioactive isotope to decay per unit of time.

A higher value for the decay constant signifies a quicker rate of decay.

The decay constant is crucial for calculating the activity, which represents the amount of nuclei decaying every second.

Linking decay rate to number of nuclei

The activity (A) is directly proportional to the decay constant (λ) and the total number of undecayed nuclei (N):

A = λ N

Where:

• A = activity (Bq)
• λ = decay constant (s^-1)
• N = number of undecayed nuclei

Worked example - Calculating the decay constant of a radioactive sample.

A radioactive sample is identified with 3.0 x 10¹⁶ undecayed nuclei and possesses an activity of 2.4 x 10¹⁰ Bq.

Calculate the decay constant.

Step 1: Formula

λ=NA​

Step 2: Substitution and correct evaluation

λ=3.0×10162.4×1010​ = 800 x 10−9 s−1

The relationship between half-life and decay constant

The decay constant is related to the half-life of a radioactive sample by:

t21​​ = λln(2)​

Where:

• t21​​ = half-life (s)
• λ = decay constant (s^-1)