With this formula, we can calculate the amount \(m\) of carbon-14 over the years.Įvery year, the mass \(m\) of carbon-14 is multiplied by \(e^\) decreases by half. Substituting the initial condition \(t = 0\), \(m = 100\) gives \(C = 100\), so Since \(m\) has a continuous decay rate of \(-0.000121\), a general solution to the differential equation is ![]() Let's investigate what happens to the sample over time.įirst, we can solve the differential equation. Suppose our sample initially contains 100 nanograms of carbon-14. It turns out that, if the sample is isolated, then \(m\) and \(t\) approximately 4 satisfy the differential equation Let \(m\) be the mass of carbon-14 in nanograms after \(t\) years. Suppose we have a sample of a substance containing some carbon-14. It is naturally produced in the atmosphere by cosmic rays (and also artificially by nuclear weapons), and continually decays via nuclear processes into stable nitrogen atoms. ![]() ![]() Content Radioactive decay and half-life Decay of carbon-14Ĭarbon-14 is a radioactive isotope of carbon, containing 6 protons and 8 neutrons, that is present in the earth's atmosphere in extremely low concentrations.
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |