Half-life is a term used in chemistry to describe the amount of time it takes for a quantity of a substance to reduce to half of its initial value. This concept is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay/11%3A_Nuclear_Chemistry/11.02%3A_Half-Life). The half-life of a substance can be calculated using the following formula:
- N = N0(1/2)^n
where N is the amount of substance remaining after n half-lives, N0 is the initial amount of substance, and n is the number of half-lives that have passed/11%3A_Nuclear_Chemistry/11.02%3A_Half-Life).
The half-life of isotopes can range from fractions of a microsecond to billions of years/11%3A_Nuclear_Chemistry/11.02%3A_Half-Life). The half-life of a substance can be used to determine the amount of radioactive substance remaining after a given number of half-lives/11%3A_Nuclear_Chemistry/11.02%3A_Half-Life). The term "half-life" is almost exclusively used for decay processes that are exponential or approximately exponential.
In a chemical reaction, the half-life of a species is the time it takes for the concentration of that substance to fall to half of its initial value. In a first-order reaction, the half-life of the reactant is ln(2)/λ, where λ (also denoted as k) is the reaction rate constant.
Example: The half-life of fluorine-20 is 11.0 s. If a sample initially contains 5.00 g of fluorine-20, how much remains after 44.0 s?
If we compare the time that has passed to the isotope’s half-life, we note that 44.0 s is exactly 4 half-lives, so using the formula N = N0(1/2)^n with n = 4, we can calculate the amount of fluorine-20 remaining after 44.0 s. Substituting and solving results in the following:
- N = 5.00 g (1/2)^4 = 0.3125 g
Therefore, 0.3125 g of fluorine-20 remains after 44.0 s/11%3A_Nuclear_Chemistry/11.02%3A_Half-Life).
