Imagine a pile of oranges that slowly turn into juice over time. In the same way, unstable atomic nuclei lose energy by emitting particles or radiation. This process is called radioactive decay and it happens at a random but predictable rate.
The decay constant tells us how quickly a particular isotope decays. It is a fixed number for each isotope and has units of per second (s⁻¹). Think of λ as the “speed limit” for the decay process.
Activity is the number of decays that happen each second. It’s measured in Becquerels (Bq), where 1 Bq = 1 decay/s.
Think of activity as the “traffic” of decays: the more active a sample, the busier it is.
Here, \$A\$ is the activity, \$λ\$ is the decay constant, and \$N\$ is the number of radioactive atoms present.
So, if you know any two of these values, you can find the third.
📌 Analogy: Imagine a factory (the nucleus) that produces cars (decays). λ is the factory’s production rate per hour, N is the number of cars in the warehouse, and A is the number of cars leaving the factory each hour.
Suppose we have a sample with \$N = 5.0 \times 10^{20}\$ atoms of a certain isotope. Its decay constant is \$λ = 2.3 \times 10^{-5}\,\text{s}^{-1}\$. What is its activity?
That’s a huge activity—about 11.5 quadrillion decays per second!
| Quantity | Symbol | Units | Key Formula |
|---|---|---|---|
| Number of atoms | \$N\$ | dimensionless | — |
| Decay constant | \$λ\$ | s⁻¹ | \$λ = \frac{\ln 2}{t_{½}}\$ |
| Activity | \$A\$ | Bq (decays s⁻¹) | \$A = λN\$ |