Worked example

k=0.0693 s⁻¹ → t½=10.0 s.

Half-Life (First-Order)

Time for half of nuclei/amount to decay for first-order.

Equation

$t_{1/2}=\frac{\ln 2}{k}$

Inline: $t_{1/2}=\frac{\ln 2}{k}$$

Variables

Conditions and limitations

First-order kinetics; independent of initial amount.

Rearrangements

$k=ln2/t½$

Dimensional check: 1/s denominator → s ✓

Worked example

k=0.0693 s⁻¹ → t½=10.0 s.

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

Common errors

• Using for non-first-order
• Half-life meaning half disappears forever

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.