Half-Life Calculator

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.

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.

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.

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.

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.

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.