Examples of half-life in the following topics:
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- The half-life of a radionuclide is the time taken for half the radionuclide's atoms to decay.
- The half-life of a radionuclide is the time taken for half of the radionuclide's atoms to decay.
- A half-life must not be thought of as the time required for exactly half of the atoms to decay.
- Note that after one half-life there are not exactly one-half of the atoms remaining; there are only approximately one-half left because of the random variation in the process.
- The problems are taken from "The Joy of Physics. " This one deals with radioactive half-life.
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- Carbon-14 has a relatively short half-life of 5,730 years, meaning that the fraction of carbon-14 in a sample is halved over the course of 5,730 years due to radioactive decay to nitrogen-14.
- Describes radioactive half life and how to do some simple calculations using half life.
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- Because of this exponential nature, one of the properties of an isotope is its half-life, the time by which half of an initial number of identical parent radioisotopes have decayed to their daughters.
- Half-lives have been determined in laboratories for thousands of radioisotopes (radionuclides).
- These half-lives can range from nearly nonexistent spans of time to as much as $10^{19}$ years or more.
- When equilibrium is achieved, a granddaughter isotope is present in proportion to its half-life.
- But, since its activity is inversely proportional to its half-life, any nuclide in the decay chain finally contributes as much as the head of the chain.
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- Because of this, the present activity on Earth from uranium-238 is only half as much as it originally was because of its 4.5-billion-year half-life.
- Potassium-40 (with a half-life of 1.25 billion years) is at about eight percent of its original activity.
- This is because humans evolved too recently for the difference in activity over a fraction of a half-life to be significant.
- Put another way, human history is so short in comparison to a half-life of a billion years that the activity of these long-lived isotopes has been effectively constant throughout our time on this planet.
- Many shorter-half-life and therefore more intensely radioactive isotopes have not decayed out of the terrestrial environment because they are still being produced.
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- Also, only four naturally occurring, radioactive odd-odd nuclides have a half-life greater than a billion years:
- All elements form a number of radionuclides, although the half-lives of many are so short that they are not observed in nature.
- For every chemical element, many radioisotopes that do not occur in nature (due to short half-lives or the lack of a natural production source) have been produced artificially.
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- In nature, most isotopes are beta-stable, but there exist a few exceptions with half-lives so long that they have not had enough time to decay since the moment of their nucleosynthesis.
- One example is the odd-proton odd-neutron nuclide 40 K, which undergoes both types of beta decay with a half-life of 1.277 ยท109 years.
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- Water waves can be commonly observed in daily life, and comprise both transverse and longitudinal wave motion.
- When waves propagate in shallow water (where the depth is less than half the wavelength), the particle trajectories are compressed into ellipses.
- Deep water corresponds with a water depth larger than half the wavelength, as is a common case in the sea and ocean.
- The deep-water group velocity is half the phase velocity.
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