Page 62 - Petrophysics 2E

36 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

TABLE 2.2
RADIOACTIVE ELEMENTS, THEIR HALF-LIVES AND RADIOACTIVE DECAY
“DAUGHTER” ELEMENTS [3]
Elem en t Half-life Stable Daughter

Carbon- 14 5,710 years Nitrogen-14
Potassium40 1.3 billion years Argon-40
ThOfiUm-232 13.9 billion years Lead-208
Uranium-23 5 0.7 1 billion years Lead-207
Uranium-238 4.5 billion years Lead-206

characterized by the following equations:

Ct = In (No/Nt)
Ctlp = In (1.0/0.5) = 0.693 (2.3)

ti12 = 0.693/C

where: C = radioactive decay constant.
No = original amount of parent element.
Nt = amount of daughter isotope currently present.
t1p = half-life of the parent element.
t = age, years

Dating early events from the decay of carbon-14 is possible because the
radiocarbon is formed in the atmosphere by collision of cosmic rays with
nitrogen. The carbon dioxide in the atmosphere thus contains a small
amount of radiocarbon and, therefore, all plants and animals contain
carbon-14 along with the stable carbon-12. When the plant or animal
dies, the accumulation of carbon-14 stops and its content of radiocarbon
decays steadily. The carbon dating is then made possible by measuring
the ratio of 14C to 12C in the remains of organism and comparing it
to the ratio of these isotopes in current living plants or animals; for
example, if the relative radiocarbon content of a specimen of bone
[(14C/’2C)dead/(14C/12C)living] is one-fourth that of the modern specimen,
the age of the specimen is 11,420 years. This is because 1/4 = 1/2 x 1/2
of two half-lives (2 half-lives x 5,710 years/half-life = 11,420 years).

EXAMPLE

If 0.35 grams of N-14 per 1.0 grams of C-14 is found in a sediment,
determine the age of the sediment.