In this equation, the units of measure for N and No can be in grams, atoms, or moles.
It does not matter as long as they are like measures.
The method of carbon dating makes use of the fact that all living organisms contain two isotopes of carbon, carbon-12, denoted 12C (a stable isotope), and carbon-14, denoted 14C (a radioactive isotope).
The ratio of the amount of 14C to the amount of 12C is essentially constant (approximately 1/10,000).
Research has been ongoing since the 1960s to determine what the proportion of in the atmosphere has been over the past fifty thousand years.
The resulting data, in the form of a calibration curve, is now used to convert a given measurement of radiocarbon in a sample into an estimate of the sample's calendar age.
If you could watch a single atom of a radioactive isotope, U-238, for example, you wouldn’t be able to predict when that particular atom might decay.
It might take a millisecond, or it might take a century. But if you have a large enough sample, a pattern begins to emerge.
It takes a certain amount of time for half the atoms in a sample to decay.
This decay is an example of an exponential decay, shown in the figure below.
Knowing about half-lives is important because it enables you to determine when a sample of radioactive material is safe to handle.
Now, take the logarithm of both sides to get $$ -0.693 = -5700k, $$ from which we can derive $$ k \approx 1.22 \cdot 10^.