☢️ Half-Life Calculator

Calculates the amount of substance remaining over time based on the half-life of radioactive isotopes.

Remaining Amount

—

Decay Percentage — Half-Lives Passed —

指南

瞭解更多

What is Half-Life?

Half-life is the time required for a radioactive substance to reduce to half of its initial amount. For example, carbon-14 has a half-life of about 5,730 years, meaning that after 5,730 years, only half of the original amount remains. Each radioactive isotope has its own unique half-life, which is constant and unchanging.

Half-Life Calculation Formula

The remaining amount is calculated using the formula N(t) = N₀ × (1/2)^(t/t₁/₂). Where N(t) is the amount after time t, N₀ is the initial amount, t is elapsed time, and t₁/₂ is the half-life. For example, a substance with initial amount 100g and half-life 10 days will have 50g after 10 days, 25g after 20 days, and 12.5g after 30 days.

Radiocarbon Dating

In archaeology, the half-life of carbon-14 is used to date organic materials. Living organisms absorb carbon-14, but after death, they no longer absorb it and it only decays. By measuring the amount of remaining carbon-14, we can estimate the time of death. This method can date artifacts up to about 50,000 years old.

Half-Life Applications in Medicine

Nuclear medicine uses radioactive isotopes like iodine-131 (half-life 8 days) and technetium-99m (half-life 6 hours) for diagnosis and treatment. Iodine-131 used for thyroid cancer treatment has an appropriate half-life that provides therapeutic effects while minimizing long-term radiation exposure. Dosage and timing are determined based on half-life considerations.

Half-Lives of Various Isotopes

Different radioactive isotopes have vastly different half-lives. Uranium-238: 4.5 billion years, plutonium-239: 24,000 years, cesium-137: 30 years, iodine-131: 8 days, radon-222: 3.8 days, technetium-99m: 6 hours. Short half-life isotopes are mainly used for medical diagnosis, while long half-life isotopes are used for geological dating.

Radioactive Waste and Half-Life

The disposal of radioactive waste from nuclear power plants is closely related to half-life. Plutonium-239 has a half-life of 24,000 years, so it takes about 10 half-lives (approximately 240,000 years) to reach safe levels. For this reason, high-level radioactive waste must be stored deep underground for long periods, and waste management strategies considering half-life are essential.

常見問題

What is the formula used for half-life decay?

The remaining amount is calculated as N(t) = N₀ × (1/2)^(t/t½). Enter the initial amount, half-life, and elapsed time to instantly see the remaining amount and decay percentage.

What if the elapsed time and half-life use different time units?

You can select a time unit (seconds, minutes, hours, days, or years) for the calculator. Make sure the half-life and elapsed time are entered in the same unit, or convert them first, since mismatched units will produce an incorrect result.

What does "half-lives passed" mean?

It is the elapsed time divided by the half-life, showing how many times the substance has been cut in half. For example, a value of 2 means the substance has gone through two half-lives and only 1/4 of the original amount remains.

Does the remaining amount ever reach exactly zero?

No, mathematically the amount only decreases exponentially and never reaches exactly zero. After about 10 half-lives, however, the remaining amount drops below roughly 0.1% of the original and becomes practically negligible.

Where is this calculator commonly used?

It applies to fields like archaeological dating with carbon-14, nuclear medicine diagnostics using isotopes such as iodine-131 or technetium-99m, and radioactive waste management planning.