Half-life

Radioactive isotopes decay spontaneously; that is, the decay reaction occurs randomly without outside influences. If we look at the nucleus of a radioactive isotope, we do not know when it will undergo radioactive decay. It could be in the next second, a few minutes from now, or in days, years, centuries—or even in a few millennia. In the macroscopic world, the forces of gravity and electromagnetism are deterministic, meaning that we can write down the equations and can calculate exactly how every object moves and interacts with the environment. In the microscopic world of the nucleus, however, the weak force and the decay of radioactive atoms is statistical, not deterministic. This is one way in which our everyday world and the quantum world are fundamentally different. Read the text aloud
Half-life decay of a sample of 16 atomsThe number of atoms that will decay radioactively in a fixed period of time is determined by the isotope’s half-life. In the time period of one half-life, half of those radioactive atoms will undergo radioactive decay. The half-life is denoted by the symbol t½. Imagine that you have 16 atoms of the same radioactive isotope and it has a half-life of one hour. After one hour, half of those atoms—eight of them—will have decayed, while the other eight are unchanged. Now wait another hour. Of the eight previously undecayed atoms, half of them—four more atoms—will decay in this second hour, while the other four atoms are still unchanged. Wait again for an hour. At the end of this third hour, half of the four undecayed atoms—two more atoms—will have decayed, while the other two still stay the same. That is how half-life works: After the time period of one half-life, half of the atoms will have decayed radioactively. Read the text aloud Show Was Einstein wrong?
Half-life for various nuclidesSome radioactive isotopes have a very short half-life, whereas others have a half-life of billions of years. For example, uranium-238 has a half-life of 4.5 billion years and so it has been around since the formation of our Solar System. Iodine-131 and cesium-137 are radioactive products of nuclear fission. Fluorine-18, which is a isotope used in positron emission tomography (PET), has a half-life of about 110 minutes and so it does not occur naturally. Isotopes with very short half-life are generated in the laboratory. Read the text aloud
Carbon-14 decayEvery half-life, the number of radioactive nuclei decreases by half. The number of carbon-14 nuclei in a sample will decrease by half every 5,730 years. As carbon-14 decays via beta decay, nitrogen-14 is generated. Read the text aloud
After a tree dies, the carbon-14 in it stops being replenished and starts decaying. After 11,460 years, what percentage of carbon-14 is left?
  1. 12.5%
  2. 25%
  3. 50%
  4. 100%
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