Applying the Radiocarbon Decay Curve
Page 5 of 12
The half-life of C-14 is 5730 years. A sample that has decayed for three half-lifes is 3 x 5730 years or 17,190 years old.
To determine how much C-14 is in a sample, radiation detectors count the number of BETA particles released by radioactive decay. The result is called the ACTIVITY (disintigrations per minute per gram of carbon--dpm/g). Modern samples have an activity of about 12.5 dpm/g. Older samples have values less than the modern value. C-14 measurements are often expressed as "% modern", which is the ratio of sample activity to modern activity. For example, a % modern value of 25% means that the sample contains 25% of its initial C-14.
The sample size required for this method depends on the type of material, but is generally in the tens to hundreds of grams range. Very small samples just don't have enough C-14 to be reliably measured. The smallest C-14 activity measurable with most methods is about 0.2 % modern, which corresponds to about 9 half-lives.
A Few Questions to Answer
Drag your mouse pointer on the red dot of C-14 decay curve below to see how % C-14 remaining and half-life are related. With 60% parent remaing, the half-life value should be a little over 0.7. Use the C-14 decay curve and the calculator to help you answer the study questions. The calculator has the Half-life of C-14 (5730 years) built-in and allows you to convert fractions of Half-lives to years. For example a sample with only 90% residual C-14 is about 0.16 HL old, which from the calculator is over 900 years.
 
1. About what percent of modern C-14 remains in a sample that is two half-lives old?
 
  2% 12%
  3 % 10%
  25%  
2. What percent of modern C-14 remains in a sample that is five half-lives old?
  2% 3% 5% 25% 50%
3. What is the approximate age, in years, of a sample that contains 90 % of its original C-14?
  900 1950 3000 5000 27500
4. What is the approximate age, in years, of a sample that contains 30 % of its original C-14?
  4500 6200 7303 9700 15500
5. What is the approximate age, in years, of a sample that contains 3 % of its original C-14?
  850 1750 3000 5000 28000
6. 0.2% is the smallest activity that a sensitive detector can measure from the emitted beta particles of C-14 decay. Using this value, what is the approximate maximum age in years that can be determined with the C-14 method?
  52,000 57,300 69,000 74,000 80,000

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