Radioactive Decay Law

📊 intermediate

$$N(t) = N_0 e^{-\lambda t}$$

Predicts the number of radioactive nuclei remaining after a certain time.

Variables & Units

$N(t)$

Quantity remaining after time $t$

Unit: Dimensionless (Count)

$N_0$

Initial quantity

Unit: Dimensionless (Count)

$\lambda$

Decay constant

Unit: $s^{-1}$

$t$

Elapsed time

Unit: Seconds ($s$)

Key Information

📐 Derived From

Differential equation $dN/dt = -\lambda N$.

💡 Example

Carbon dating an ancient artifact.

🔧 Applications

Medical imaging and archeology.

⚠️ Constraints

Statistical law valid for large numbers of atoms.

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