25.2. Radioactive Half-life http://www.ck12.org
Decay of Carbon-14
This function tells us how to measure the time taken by the decay of carbon-14. At the onset of death, the carbon-
14 in the body begins to decrease. While a living thing is alive, it has a fixed ratio of carbon-14 to the ordinary
carbon-12 of roughly one part per trillion.
Carbon-14 has a half-life of 5,730 years. Thus, after 5,730 years, only about half of the carbon-14 will remain (one
part per two trillion). After 11,460 years, the ratio will be one part per four trillion.
Radioactive dating (or just carbon dating) is not perfect because the processes which form radioactive carbon and
mix it with nonradioactive carbon are very dynamic. Yet, statistically it yields fairly accurate results. The accuracy
of carbon dating has been verified by using items of known age. For example, the age assigned to papyrus found
in Egyptian pyramids using carbon dating agrees quite well with the age that historians had determined from the
historical records. Using carbon dating, the iconic paintings in Lascaux cave in southwestern France have been
determined to be around 15, 500 ±900 years old. Carbon dating techniques have been instrumental in determining
the approximate ages of prehistoric settlements by an examination of the charcoal found at campsites.
Learn more about carbon dating at the link below.
http://demonstrations.wolfram.com/CarbonDating/
Illustrative Example
A sample of 128 grams of a radioactive isotope with half-life of 8 years decays for 48 years. How much of the
original isotope remains?
Solution:
The time period for the decay, 48 years, is equivalent to 6 half-lives (or six doublings)→n=^488 =6.
Using Equation A,
N=
( 1
2)n
No=( 1
2) 6
( 128 g) = 2. 00 gTherefore after 48 years, 2.00 g of the original isotope remains.
b. Determine the amount remaining if the time is 50 years.
Solution:
The approach is the same as in part (a).
n=^508 = 6 .25 doublings
N=
( 1
2)n
No=( 1
2) 6. 25
( 128 g) = 1. 68 g