Radioactive Decay Calculator

Calculate radioactive decay and half-life for any isotope. Find remaining amounts, time elapsed, or determine half-life from decay data. Supports common isotopes like Carbon-14.

Initial quantity of radioactive material

Half-life of the isotope

Time since initial measurement

Remaining percentage or amount

Radioactive Decay Formula: N(t) = N₀ × 2^(-t/t½) Where: • N(t) = Remaining amount after time t • N₀ = Initial amount • t = Time elapsed • t½ = Half-life Alternative Form: N(t) = N₀ × e^(-λt) where λ = ln(2) / t½ ≈ 0.693 / t½ Key Relationships: • After 1 half-life: 50% remains • After 2 half-lives: 25% remains • After 3 half-lives: 12.5% remains • After n half-lives: (0.5)^n × 100% remains
Example 1 (Carbon-14 Dating): Half-life = 5730 years Initial = 100% Time = 5730 years Remaining = 100 × 0.5^1 = 50% Example 2 (Uranium-238): Half-life = 4.5 billion years Initial = 10 g Time = 9 billion years (2 half-lives) Remaining = 10 × 0.5² = 2.5 g Example 3 (Iodine-131): Half-life = 8 days Initial = 100 mCi Time = 24 days (3 half-lives) Remaining = 100 × 0.5³ = 12.5 mCi Example 4 (Calculate Time): Half-life = 30 years Initial = 100% Remaining = 12.5% n = -log₂(0.125) = 3 half-lives Time = 3 × 30 = 90 years Example 5 (Short-lived Isotope): Half-life = 2 minutes Initial = 1 Ci Time = 10 minutes (5 half-lives) Remaining = 1 × 0.5^5 = 0.03125 Ci

What is radioactive decay?

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. Each radioactive isotope has a characteristic half-life - the time required for half of the atoms in a sample to decay. Common isotopes include Carbon-14 (5730 years), Uranium-238 (4.5 billion years), and Iodine-131 (8 days).

How does the half-life affect calculations?

The half-life determines how quickly a radioactive isotope decays. Shorter half-lives mean faster decay and more intense radiation initially. The formula N(t) = N₀ × (0.5)^(t/t½) calculates remaining amount, where t is elapsed time and t½ is half-life. After n half-lives, amount = initial × (0.5)^n.

What is carbon dating?

Carbon-14 dating uses the 5730-year half-life of carbon-14 to determine the age of organic materials up to about 50,000 years old. Living organisms maintain a constant C-14 to C-12 ratio. When they die, C-14 decays without replacement, allowing scientists to estimate the time since death by measuring remaining C-14.

How do you calculate remaining amount after decay?

Use the formula: Remaining = Initial × 2^(-time/half-life). For example, 100 g of Carbon-14 after 11,460 years (2 half-lives): Remaining = 100 × 2^(-2) = 100 × 0.25 = 25 g. After 5 half-lives, only 3.125% remains.

What is the decay constant (lambda)?

The decay constant λ relates to half-life by λ = ln(2) / t½ ≈ 0.693 / t½. It represents the probability per unit time that a single atom will decay. Higher λ means faster decay. Activity (decays per second) = λ × N, where N is the number of atoms.

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