Radioactive isotopes decay exponentially. They all decrease by giving off and thereby losing energy and matter particles, but each radioactive isotope is characterized by its own respective rate of decay. The rate at which radioactive isotopes decay is measured in terms of “half-lifes”. A half-life of an isotope is defined as the amount of time that it takes for one-half of its quantity of atoms to reduce.
Simply by knowing the half-life of radiocarbon can you calculate its constant rate of decay, create a mathematical model of its decay, and then be able to figure out the age of nearly any deceased organism that contains it!
One significant limitation, however, of the model and of the use of radiocarbon for dating fossils is carbon-14’s relatively short half-life length. Because the isotope decays so quickly, it is often very difficult to detect traces of it in artifacts over 50,000 years old. In such cases and those much older, it is necessary to date fossils using isotopes with longer half-lives, such as uranium-238 with a half-life of 4.5 billion years. Still however, as long as the half-life of the isotope is known, it
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I began with an investigation of isotope “half-lives” and derived an exponential equation for a pattern that presented itself while I was observing the effect of radioactive decay of a general isotope on the quantity of that isotope in an organism. I then made my calculations specific to carbon-14, typically used for dating fossils, and used the general equation along with knowledge of radiocarbon’s half-life length, to solve for that isotope’s constant rate of decay. In doing so, I was able to succeed in creating a mathematical model (algebraic and graphical) of the exponential decay of carbon-14 and applying it to innumerable other scenarios, such as dating fossils. As such, I believe that my methods were successful and