Worked example

After 2 half-lives, N=N0/4.

Radioactive Decay Law

Amount remaining after time t via exponential decay.

Equation

$N = N_0 e^{-kt}, \ln\frac{N_0}{N}=kt$

Inline: $N = N_0 e^{-kt}, \ln\frac{N_0}{N}=kt$$

Variables

Symbol	Quantity	Unit	Notes
$N$	remaining nuclei	—	—
$N0$	initial nuclei	—	—
$k$	decay constant	s⁻¹	—
$t$	time	s	—

Conditions and limitations

First-order decay.

Rearrangements

$t=(1/k)ln(N0/N)$

Dimensional check: dimensionless exponent ✓

Worked example

After 2 half-lives, N=N0/4.

Steps: write equation → substitute with units → check dimensional consistency → report with correct significant figures.

Common errors

• Linear instead of exponential

Related resources

• nuclear-chemistry topic
• Calculators — linked only when a real calculator implements this formula.
• Constants — sourced constants with version when values are required.

Sources

• NIST Physical Constants 2022 — CODATA.

Reviewed 2026-08-21 by Editorial Team; due 2027-08-21.