# Half-life (element)

mean duration after which a decaying quantity has reached half of its initial value

The half-life of a substance is the time it takes for half of the substance to decay. The word "half-life" was first used when talking about radioactive elements where the number of atoms get smaller over time by changing into different atoms. It is now used in many other situations where something declines exponentially, like the time it takes for a drug in the body to be half gone. A Geiger-Muller detector can be used to measure the radioactive half-life; it is the time when the activity is half of the original.

Simulation of many identical atoms undergoing radioactive decay, starting with either 4 atoms per box (left) or 400 (right). The number at the top is how many half-lives have elapsed. Note the law of large numbers: With more atoms, the overall decay is more regular and more predictable.
Number of
half-lives
that have happened
Parts
remaining
As
power
of 2
0 1/1 ${\displaystyle 1/2^{0}}$
1 1/2 ${\displaystyle 1/2^{1}}$
2 1/4 ${\displaystyle 1/2^{2}}$
3 1/8 ${\displaystyle 1/2^{3}}$
4 1/16 ${\displaystyle 1/2^{4}}$
5 1/32 ${\displaystyle 1/2^{5}}$
6 1/64 ${\displaystyle 1/2^{6}}$
7 1/128 ${\displaystyle 1/2^{7}}$
8 1/256 ${\displaystyle 1/2^{8}}$
9 1/512 ${\displaystyle 1/2^{9}}$
10 1/1024 ${\displaystyle 1/2^{10}}$
... ...
${\displaystyle N}$ ${\displaystyle 1/2^{N}}$ ${\displaystyle 1/2^{N}}$

Half-life depends on probability because the atoms decay at a random time. Half-life is the expected time when half the number of atoms have decayed, on average. Carbon-14 has a half-life of 5,730 years. Taking one atom of carbon-14, this will either have decayed after 5,730 years, or it will not. But if this experiment is repeated again and again, it will be seen that the atom decays within the half life 50% of the time.

Radioactive isotopes are atoms that have unstable nuclei, meaning that the nucleus of each atom will decay after enough time has passed. Their nuclei are unstable because the arrangement of protons and neutrons in them are unsteady. This decay, which means they change into completely different types of atoms. This is known as radioactive decay. When they decay, they release particles such as alpha particles, beta particles, gamma rays. Sometimes they decay by fission, which means to break into pieces, to make smaller nuclei. For example, a radioactive carbon-14 atom releases a beta particle to become nitrogen-14. As an example of fission decay, a fermium-256 atom can split into xenon-140 and palladium-112 atoms, releasing four neutrons in the process.

For example, uranium-232 has a half-life of about 69 years. Plutonium-238 has a half-life of 88 years. Carbon-14, which is used to find the age of fossils, has a half-life of 5,730 years.

After ten half-lives, about 99.9% of the atoms have decayed into different atoms, so only 0.1% of the original atoms are left, and 99.9% of the radioactivity from the original kind of atom is gone. Some atoms decay into other atoms that are also radioactive, so the remaining radioactivity depends on the type of atom.