Half-life and radioactive dating methods
Source:
http://www.navsea.navy.mil/Portals/103/Documents/NNPTC/Radiation/doe_reactor_theory_v1.pdf
Radioactive Decay Rates
Radioactivity is the property of certain nuclides of spontaneously emitting particles or gamma
radiation. The decay of radioactive nuclides occurs in a random manner, and the precise time
at which a single nucleus will decay cannot be determined. However, the average behavior of
a very large sample can be predicted accurately by using statistical methods. These studies have
revealed that there is a certain probability that in a given time interval a certain fraction of the
nuclei within a sample of a particular nuclide will decay. This probability per unit time that an
atom of a nuclide will decay is known as the radioactive decay constant, λ. The units for the
decay constant are inverse time such as 1/second, 1/minute, 1/hour, or 1/year. These decay
constant units can also be expressed as second-1, minute-1, hour-1, and year-1.
Variation of Radioactivity Over Time
The rate at which a given radionuclide sample decays is stated in Equation (1-3) as being equal
to the product of the number of atoms and the decay constant. From this basic relationship it
is possible to use calculus to derive an expression which can be used to calculate how the
number of atoms present will change over time. The derivation is beyond the scope of this text,
but Equation (1-4) is the useful result.
(1-4)
where:
N = number of atoms present at time t
N = number of atoms initially present o
= decay constant (time )-1
t = time
1. How long has radioactive decay been measured?
2. How is the half-life determined?
3. What is an average and what statistical methods are used to determine an average?
4. What variables must be assumed in using a half-life to determine dates?
5. In what way does this dating method assume uniformity?
6. What changes or alterations might affect the variables of this equation and how might that affect dating methods?
