For each pair of students, you will need: Context This is the second lesson in a three-lesson series about isotopes, radioactive decay, and the nucleus. The first lesson, Isotopes of Pennies , introduces the idea of isotopes. An Analogy to Carbon Dating , is based on gathering evidence in the present and extrapolating it to the past. To do this lesson and understand half-life and rates of radioactive decay, students should understand ratios and the multiplication of fractions, and be somewhat comfortable with probability. Games with manipulative or computer simulations should help them in getting the idea of how a constant proportional rate of decay is consistent with declining measures that only gradually approach zero.
For this example, the term half time might be used instead of “half life”, but they mean the same thing. It varies depending on the atom type and isotope , and is usually determined experimentally. See List of nuclides.
What Is Half-Life? Half-life is defined as the time it takes for one-half of a radioactive element to decay into a daughter isotope. As radioactive isotopes of elements decay, they lose their radioactivity and become a brand new element known as a daughter isotope.
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Half-life The half-life of a process is an indication of how fast that process proceeds—a measure of the rate or rapidity of the process. Specifically, the half-life is the length of time that it takes for a substance involved in that process to diminish to one-half of its initial amount. The faster the process, the less time it will take to use up one-half of the substance, so the shorter the half-life will be.
The rates of some biological processes, such as the elimination of drugs from the body, can be characterized by their half-lives, because it takes the same amount of time for half of the drug to disappear no matter how much there was to begin with. Processes of this kind are called first-order processes. On the other hand, the speeds of many chemical reactions depend on the amounts of the various substances that are present, so their rates cannot be expressed in terms of half-lives; more complicated mathematical descriptions are necessary.
Half-lives are most often heard of in connection with radioactive decay —a first-order process in which the number of atoms of a radioisotope a radioactive isotope is constantly diminishing because the atoms are transforming themselves into other kinds of atoms. In this sense, the word “decay” does not mean to rot; it means to diminish in amount. If a particular radioisotope has a half-life of one hour, for example, then at 3 p.
The amount of the radioactive material thus gets smaller and smaller, but it never disappears entirely.
The Radiometric Dating Game
Back to The Dating Game Here’s an example of how half-life works: Let’s say you have 80 ants, and these ants have a half-life of ten days. In ten days, then, 40 of your ants would still be alive. Ten days after that, 20 ants would still be alive. Ten more days, and ten would be alive.
In these cases, usually the half-life of interest in radiometric dating is the longest one in the chain, which is the rate-limiting factor in the ultimate transformation of the radioactive nuclide into its stable daughter.
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Because the half-life of carbon is 5, years, it is only reliable for dating objects up to about 60, years old. However, the principle of carbon dating applies to other isotopes as well. Potassium is another radioactive element naturally found in your body and has a half-life of billion years.
See some updates to this article. We now consider in more detail one of the problems with potassium-argon dating, namely, the branching ratio problem. Here is some relevant information that was e-mailed to me. There are some very serious objections to using the potassium-argon decay family as a radiometric clock. The geochronologist considers the Ca40 of little practical use in radiometric dating since common calcium is such an abundant element and the radiogenic Ca40 has the same atomic mass as common calcium.
Here the actual observed branching ratio is not used, but rather a small ratio is arbitrarily chosen in an effort to match dates obtained method with U-Th-Pb dates. The branching ratio that is often used is 0. Thus we have another source of error for K-Ar dating.
Uranium (U) Isotope Decay Calculator
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Half-life (symbol t 1⁄2) is the time required for a quantity to reduce to half its initial value. The original term, half-life period, dating to Ernest Rutherford’s discovery of the principle in , was shortened to half-life in the early s.
Generally, there are four main concepts that students struggle with when thinking about radioactive decay: A steady but unpredictable spontaneous process Radioactivity and radioactive decay are spontaneous processes. Students often struggle with this concept; therefore, it should be stressed that it is impossible to know exactly when each of the radioactive elements in a rock will decay. Statistical probablity is the only thing we can know exactly.
Often students get bogged down in the fact that they don’t “understand” how and why radioactive elements decay and miss the whole point of this exercise. If they can begin to comprehend that it is random and spontaneous, they end up feeling less nervous about the whole thing. Radioactive decay involves the spontaneous transformation of one element into another.