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So what we do is we come up with terms that help us get our head around this. So I wrote a decay reaction right here, where you have carbon-14. So now you have, after one half-life-- So let's ignore this. I don't know which half, but half of them will turn into it. And then let's say we go into a time machine and we look back at our sample, and let's say we only have 10 grams of our sample left. Now you could say, OK, what's the probability of any given molecule reacting in one second? But we're used to dealing with things on the macro level, on dealing with, you know, huge amounts of atoms. So I have a description, and we're going to hopefully get an intuition of what half-life means. And how does this half know that it must stay as carbon? So if you go back after a half-life, half of the atoms will now be nitrogen. Then all of a sudden you can use the law of large numbers and say, OK, on average, if each of those atoms must have had a 50% chance, and if I have gazillions of them, half of them will have turned into nitrogen. How much time, you know, x is decaying the whole time, how much time has passed? Any animal that eats a plant ingests a mixture of organic compounds that contains approximately the same proportions of carbon isotopes as those in the atmosphere.When the animal or plant dies, the carbon-14 nuclei in its tissues decay to nitrogen-14 nuclei by a radioactive process known as beta decay, which releases low-energy electrons (β particles) that can be detected and measured: \[ \ce \label\] The half-life for this reaction is 5700 ± 30 yr. Comparing the disintegrations per minute per gram of carbon from an archaeological sample with those from a recently living sample enables scientists to estimate the age of the artifact, as illustrated in Example 11.In a first-order reaction, every half-life is the same length of time. Calculate the half-life for the hydrolysis reaction under these conditions.If a freshly prepared solution of cis-platin has a concentration of 0.053 M, what will be the concentration of cis-platin after 5 half-lives? What is the percent completion of the reaction after 5 half-lives? Given: rate constant, initial concentration, and number of half-lives Asked for: half-life, final concentrations, and percent completion Strategy: Radioactivity, or radioactive decay, is the emission of a particle or a photon that results from the spontaneous decomposition of the unstable nucleus of an atom.
In any sample of a given radioactive substance, the number of atoms of the radioactive isotope must decrease with time as their nuclei decay to nuclei of a more stable isotope.
Using Activity is usually measured in disintegrations per second (dps) or disintegrations per minute (dpm).
The activity of a sample is directly proportional to the number of atoms of the radioactive isotope in the sample: \[A = k N \label\] Here, the symbol is the same as the equation for the reaction rate of a first-order reaction, except that it uses numbers of atoms instead of concentrations.
This is not true for zeroth- and second-order reactions.
The half-life of a first-order reaction is independent of the concentration of the reactants.
Let's say I have a bunch of, let's say these are all atoms. And let's say we're talking about the type of decay where an atom turns into another atom. Or maybe positron emission turning protons into neutrons. And we've talked about moles and, you know, one gram of carbon-12-- I'm sorry, 12 grams-- 12 grams of carbon-12 has one mole of carbon-12 in it.