Physics for Geologists, Second edition

64 Atomic structure and age-dating
to ' 4 7 ~ through the loss of a negative @-particle: ' 2 + ~ ' 4 7 ~ + p-. All living
things absorb some 14c, but cease to do so when they die. The half-life of
radiocarbon is about 5 730 years, and dating of organic material from about
500 to 30 000 years is possible. Unfortunately, the natural balance of carbon
isotopes is being disturbed by COz from the burning of fossil fuels, which
lost their 14c long ago.
The law of radioactive decay was discovered by Rutherford and Soddy in
1902. They found that the activity of a radioactive substance decreased with
time according to the relationship
N = No ePxt, (5.1)
where No is the original number of radioactive atoms and N is the number
after time t (Figure 5.2). The material constant h is known nowadays as the
decay constant, and its inverse (111 = t) is known as the mean life. Differentiating,
dN/dt = -1 No ecxt = -h N, and the rate of decrease of the number
of radioactive atoms is proportional to their number. (Note that this would
have been a reasonable postulate, and integration would have led to the same
equation.) No known agency, physical or chemical, can control the rate of
decay except bombardment by other particles. It is purely a matter of chance.
Equation 5.1 leads to an expression in terms of half-life, till, without
involving X explicitly:
but h is hidden in there in tll2 = In (0.5)/(-X). Measurement of the concen-
trations of parent and daughter nuclides in minerals and rocks by chemical
or physical means enables geochemists to determine the age of the minerals
or rocks. The age represents the time at which the mineral or rock became
a closed chemical system as regards the nuclides concerned.
There are some important assumptions made in the determination of so-
called absolute dates or ages from isotope analysis. These are:
1 that the daughter did not exist at time zero when the parent nuclide was
formed;
2 that the decay constant is in fact a constant, and is reasonably accurately
known;
3 that nothing can significantly alter the decay rate;
4 that parent and daughter can be measured accurately, and that their
quantities have not been altered by leakage or addition.
Assumption (1) is implicit in the equations. Assumptions (2) and (3) are
supported by theory and experiment. Assumption (4) is necessary, and consistent
results tend to support it. Special care has to be taken with the
measurement of gases, as in the potassium-to-argon decay, and any leakage
is usually detected by inconsistent results when checked by other methods.
Does a half-life of 48.8 x lo9 years for 87~b mean that the universe is at
least that old? . . . or will last that long?
Copyright 2002 by Richard E. Chapman