# Half-life

The half-life (t½) is the time for a reactant's concentration to fall to half. For a first-order reaction, t½ = 0.693/k, and it is the same no matter how much you start with. Zero and second order half-lives do change.

Chemistry (university) · Part 06: Chemical kinetics · Card 5 of 9 · Last updated 2026-10-19

## Analogy

Like a bar of chocolate you eat half of each hour: half the remaining chocolate is gone every time.

## Example

**First-order drug**

k = 0.0231 min⁻¹
t½ = 0.693 / 0.0231 = 30.0 min
After 90 min: 3 half-lives
Fraction left = (½)³ = 1/8

## In practice

Carbon-14 has a half-life of about 5730 years, which archaeologists use to date old wood and bone.

## Practice

### Flashcards

- **Half-life formula for first order?** t½ = 0.693/k.

## Questions people ask

### Why is first-order half-life constant?

In first-order decay, the rate is proportional to the amount left. Halving the amount halves the rate, so the time to lose the next half stays the same. This is why t½ = 0.693/k does not depend on the starting concentration.

### How many half-lives until a reaction is basically over?

After 5 half-lives, about 3 percent of the reactant remains, and after 7, less than 1 percent. Chemists often treat a first-order reaction as complete after 7 to 10 half-lives. The reactant never reaches exactly zero, because each half-life removes only half.

## Related concepts

- [First-order integrated rate law](https://studyvisually.com/learn/science/chemistry-university/chemistry-university-part-6/chemistry-university-part-6-concept-4)

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