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Radioactive decay law
Intermediate
Number of nuclei decays exponentially.
N = N₀e^{−λt}N = N₀e^{−λt} and the activity A = λN. Decay is random for individual nuclei but exact statistically.
After 3 half-lives 12.5% remain.
Rate doesn't depend on temperature or chemistry.
In more detail
The radioactive decay law states that the number of nuclei decreasing per unit time is proportional to the number present, N = N0 e^(−λt). This gives an exponential decay.
Real-world uses
- Decay curves are used to predict activity of samples.
- Medical physicists calculate dose from decay laws.
- Physicists predict how many radioactive nuclei remain after a given time, which is essential for dating and shielding.
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Frequently asked questions
What is the decay constant?
The probability per unit time that a nucleus decays.
Does the decay depend on age?
No, each nucleus has a constant probability of decaying regardless of age.
Why is radioactive decay random for each nucleus?
Quantum mechanics gives only the probability of decay for each nucleus, while the average over many nuclei follows the exponential law.
Related topics in Atomic & Nuclear Physics
Alpha decay · Beta decay · Gamma decay · Half-life · Mean life · Activity