Exponential Radioactive Decay
For a single radioactive species with constant decay constant lambda and no production, dN/dt = -lambda N and N(t) = N0 exp(-lambda t). Activity is the positive decay rate A = -dN/dt = lambda N.
Why this shows up in the exam
Finding undecayed fraction · Interpreting semilog decay plots · Comparing activities at different times
Learn the idea
Independent nuclei with constant decay probability produce exponential survival and activity. Each nucleus has the same chance per unit time of decaying, regardless of age. A constant fraction disappears in equal time intervals, so the number falls exponentially rather than linearly.
🧠 Memory hook: Radioactivity removes a fraction, not a fixed number.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- dN/dt = -lambda N — decay law for one species with constant lambda and no source
- N = N0 e^(-lambda t) — surviving radioactive nuclei after time t
- A = lambda N = A0 e^(-lambda t) — activity follows the same exponential factor
How to approach it
- 1Identify the initial quantity and elapsed time
- 2Use ratios to cancel N0 or A0
- 3Check that the result decreases for positive time
Common slip-ups that cost marks
- •Using a linear decrease
- •Dropping the minus sign in the population derivative
- •Applying one exponential to mixed species with different lambdas
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
In hydrogen, an electron transitions from n = 2 to n = 1. Using E_n = -13.6/n^2 eV, find the emitted photon energy.
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