# Radioactive dating word problems

In this section we explore half-life and activity, the quantitative terms for lifetime and rate of decay. Half of the remaining nuclei decay in the next half-life.Further, half of that amount decays in the following half-life.The following equation gives the quantitative relationship between the original number of nuclei present at time zero () and the number () at a later time : To see how the number of nuclei declines to half its original value in one half-life, let in the exponential in the equation . For integral numbers of half-lives, you can just divide the original number by 2 over and over again, rather than using the exponential relationship.For example, if ten half-lives have passed, we divide by 2 ten times. For an arbitrary time, not just a multiple of the half-life, the exponential relationship must be used. Carbon-14 has a half-life of 5730 years and is produced in a nuclear reaction induced when solar neutrinos strike in the atmosphere.The half-life of carbon-14 is approximately 5,730 years, and it can be reliably used to measure dates up to around 50,000 years ago.The process of carbon-14 dating was developed by William Libby, and is based on the fact that carbon-14 is constantly being made in the atmosphere. This means they have shorter lifetimes, producing a greater rate of decay.

All three laboratories found samples of the shroud contain 92% of the found in living tissues, allowing the shroud to be dated (see [link]).This is the exact solution; evaluate the natural log with a calculator to get the decimal approximation k = -0.000436 .Half-life is defined as the amount of time it takes a given quantity to decrease to half of its initial value.There is a tremendous range in the half-lives of various nuclides, from as short as s for the most unstable, to more than y for the least unstable, or about 46 orders of magnitude.Nuclides with the shortest half-lives are those for which the nuclear forces are least attractive, an indication of the extent to which the nuclear force can depend on the particular combination of neutrons and protons.