25.2. Radioactive Half-life http://www.ck12.org
25.2 Radioactive Half-life
Objectives
The student will:
- Understand how radioactive half-life is defined.
- Solve problems involving radioactive half-life.
- Understand radioactive dating.
- Solve problems involving radioactive dating.
Vocabulary
- carbon dating:A technique used to measure the time that the remains of an animal or plant has been dead.
By measuring how quickly the carbon-14 decays into nitrogen-14, we can measure how long the bones have
been dead. - half-life:Over the period of time of one half-life, each nucleus has a 50% chance of decaying. Every isotope
has a distinct half-life. No matter what the time duration for the half-life is, after that time interval passes,
one-half of the original sample remains.
Carbon Dating
Radioactive decay occurs spontaneously, meaning that at any given moment, some number of atoms of the original
sample (we don’t know which particular atoms) are changing into a different substance. It does not happen on a
fixed schedule, but instead happens randomly, with each atom having a chance to decay after a given time. This
can be used to measure the time that the remains of an animal or plant has been dead, using a technique known as
carbon dating.
The key to carbon dating is carbon dioxide in the air contains trace amounts of a radioactive isotope of carbon
produced in the upper atmosphere by cosmic radiation, carbon-14. It is produced in the nuclear reaction as follows:
n+^147 N→^146 C+p
As long as plants are alive, they bring in carbon-14 from the air via photosynthesis. As long as animals are alive,
they eat plants or other animals containing these trace amounts of carbon-14. Once they are dead, they are cut off
from the carbon-14 in the upper atmosphere. The remaining amount in their bones slowly goes down from decay
from beta radiation:^146 C→^147 N+β.
If we have a measure for how quickly the carbon-14 decays into nitrogen-14, this can be used to measure how long
the bones have been dead. The question is, what is that function?