define activity and decay constant, and recall and use A = λN

What is Radioactive Decay?

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.

Decay Constant (λ)

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.

• Higher λ → faster decay (shorter half‑life)
• Lower λ → slower decay (longer half‑life)

Activity (A)

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.

The Key Relationship: A = λN

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.

Example Calculation

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?

1. Write down the formula: $A = λN$
2. Insert the numbers: $A = (2.3 \times 10^{-5}\,\text{s}^{-1})(5.0 \times 10^{20})$
3. Multiply: $A = 1.15 \times 10^{16}\,\text{Bq}$

That’s a huge activity—about 11.5 quadrillion decays per second!

Exam Tips

• Always check units: λ is in s⁻¹, N is dimensionless, so A comes out in Bq.
• Remember the formula A = λN; it’s the most frequently used equation.
• When given half‑life (t½), first convert to λ using $λ = \frac{\ln 2}{t_{½}}$.
• Use the “decay constant” mnemonic: “λ” looks like a lightning bolt—fast decay means a big λ.
• Practice converting between λ, t½, and A to build confidence.