Half-Life

Half-life (t1/2) is the amount of time required for half of a given quantity of a radioactive isotope, or a reactant in certain chemical reactions, to decay or be consumed. It is one of the most useful ways to describe the stability of a radioactive substance, since it gives a fixed, predictable timeframe that doesn't depend on how much material you start with.

Every radioactive isotope has its own characteristic half-life, ranging from fractions of a second for highly unstable isotopes to billions of years for very stable ones like uranium-238. Because radioactive decay follows an exponential curve, exactly half of the remaining material decays in each successive half-life period, so after two half-lives, only a quarter of the original sample remains, and after three, only an eighth remains.

Half-life calculations are essential in fields ranging from nuclear medicine, where isotopes with short half-lives are chosen for diagnostic imaging, to archaeology, where carbon-14 dating relies on precisely known half-life values. The Half-Life Calculator computes remaining quantity, elapsed time, or half-life itself depending on which values are known.

N(t) = N0 × (1/2)^(t / t1/2)

Where:

• N(t) = amount of substance remaining after time t
• N0 = initial amount of substance
• t = elapsed time
• t1/2 = half-life of the substance

A radioactive sample starts with 80 grams of an isotope with a half-life of 10 days. How much remains after 30 days?

Number of half-lives elapsed = 30 / 10 = 3

N(t) = 80 × (1/2)^3 = 80 × 0.125 = 10 grams

After 30 days, only 10 grams of the original 80-gram sample remains, with the rest having decayed into other products. Try different starting amounts and half-life values with the Half-Life Calculator.

• Half-life is independent of sample size: Whether you start with a gram or a ton of a given isotope, the same fraction always decays during each half-life period.
• Decay is exponential, not linear: The remaining amount never quite reaches zero mathematically; it keeps halving indefinitely, which is why radioactive decay curves flatten out over many half-lives rather than dropping in a straight line.
• It differs fundamentally from activation energy: Half-life describes a fixed nuclear decay rate unaffected by temperature or catalysts, while activation energy describes a chemical reaction barrier that is highly sensitive to both.
• Half-life values span an enormous range: Some isotopes have half-lives measured in microseconds, while others, like uranium-238, have half-lives of over 4 billion years, making them useful for dating the age of rocks and the Earth itself.
• Radiometric dating relies on known half-lives: Techniques like carbon dating work only because the half-life of the relevant isotope has been measured precisely and remains constant over time.