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The decay of a radioactive
material obeys first order
kinetics. One useful measure of the radioactivity of a sample is the
activity: the number of atoms that decay in a given amount of time. The
equation for activity is
- A = k*N
where A is the activity, k the rate constant and N the
number of atoms present.
Two units are used for activity:
- Becquerel (Bq): 1 atom/sec
- Curie (Ci): 3.700*1010 atoms/sec
Obviously, the Curie
is more useful for macroscopic samples.
Example: 146C is a radioactive isotope of carbon
with a half life of 5720 years. What is the activity of a 1.00 mole sample of
carbon-14 in Becquerels?
Solution: We need to get the rate constant before we get the activity:
we use the relationship between half life and the rate constant k:
- k = 0.693/t1/2
- k = 0.693 / 5720 yr
- k = 1.21*10-4/ yr
We want the activity in terms of
seconds, not years. Converting from years to seconds will give a k =
3.84*10-12/sec. Now that we have the rate constant, simply use the
activity equation. We have 1 mole of carbon = 6.022*1023 atoms of
carbon, so
- A = k*N
- A = 3.84*10-12/ sec * 6.022*1023 atoms
- 2.31*1012 atoms/sec = 2.31*1012
Bq
This is also equal to 2.31*1012 atoms/sec * 1
Ci/3.700*1010 atoms/sec = 62.4 Ci. |