# Radioactive Decay Calculator

Calculate radioactive decay: remaining amount, fraction remaining, decay constant, and half-lives elapsed. Supports all time units from seconds to years.

## What this calculates

Calculate the remaining amount of a radioactive substance after a given time period. Uses the exponential decay formula N = N₀e^(-λt), where λ = ln(2)/t½. Supports multiple time units and displays the decay constant, fraction remaining, and number of half-lives elapsed.

## Inputs

- **Initial Amount (N₀)** — min 0 — Initial quantity of the radioactive substance (atoms, grams, Bq, Ci, or any consistent unit).
- **Amount Unit** — options: Atoms, Grams, Becquerel (Bq), Curie (Ci), Arbitrary units — Unit for the amount (for display only).
- **Half-Life Value** — min 0 — The half-life of the radioactive isotope.
- **Half-Life Unit** — options: Seconds, Minutes, Hours, Days, Years — Time unit for the half-life.
- **Elapsed Time** — min 0 — Time that has passed since the initial measurement.
- **Time Unit** — options: Seconds, Minutes, Hours, Days, Years — Time unit for the elapsed time.

## Outputs

- **Remaining Amount** — Amount of radioactive substance remaining.
- **Fraction Remaining** — Fraction of the original amount that remains (0 to 1).
- **Amount Decayed** — Amount that has decayed.
- **Half-Lives Elapsed** — Number of half-lives that have passed.
- **Decay Constant (λ)** — First-order decay constant.

## Details

Radioactive decay is a first-order process where unstable atomic nuclei spontaneously transform, emitting radiation. The rate of decay is characterized by the half-life (t½), the time for half the atoms to decay.

Key Equations

- N = N₀ × e^(-λt): Amount remaining after time t

- λ = ln(2) / t½: Decay constant (probability of decay per unit time)

- Activity = λ × N: Disintegrations per unit time (Bq or Ci)

- After n half-lives: N = N₀ / 2^n

Common Radioactive Isotopes

- Carbon-14: t½ = 5,730 years (radiocarbon dating)

- Iodine-131: t½ = 8.02 days (thyroid treatment)

- Cobalt-60: t½ = 5.27 years (radiation therapy)

- Uranium-238: t½ = 4.47 × 10⁹ years (geological dating)

- Technetium-99m: t½ = 6.01 hours (medical imaging)

Practical Applications

Radioactive decay is used in carbon dating (archaeology), radiometric dating (geology), nuclear medicine (diagnosis and treatment), smoke detectors (Am-241), and nuclear power generation. Understanding decay kinetics is essential for radiation safety and waste management.

## Frequently Asked Questions

**Q: What is a half-life?**

A: A half-life (t½) is the time required for half of a radioactive substance to decay. After 1 half-life, 50% remains. After 2 half-lives, 25% remains. After 10 half-lives, less than 0.1% remains. Half-lives range from fractions of a second to billions of years depending on the isotope.

**Q: How long until a radioactive substance is 'gone'?**

A: Theoretically, exponential decay never reaches zero. Practically, after about 10 half-lives, only 0.098% remains, which is often considered negligible. For safety purposes, 7-10 half-lives is a common guideline. For I-131 (t½ = 8 days), this means about 80 days.

**Q: What is the difference between Becquerel and Curie?**

A: Both measure activity (disintegrations per second). 1 Becquerel (Bq) = 1 disintegration per second. 1 Curie (Ci) = 3.7 × 10¹⁰ disintegrations per second (the activity of 1 gram of Ra-226). The Becquerel is the SI unit; the Curie is an older but still widely used unit.

**Q: Can environmental factors change the half-life?**

A: Nuclear decay rates are essentially independent of temperature, pressure, chemical state, or other environmental factors. The half-life is a fundamental nuclear property. Extreme conditions (like the cores of stars) can alter electron capture decay rates slightly, but these conditions do not occur on Earth.

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Source: https://vastcalc.com/calculators/chemistry/radioactive-decay
Category: Chemistry
Last updated: 2026-04-21