Back to . . . Radioactivity discovered in 1896 by French scientist Henri Becquerel and extensively investigated by Marie Curie, Pierre Curie and Ernest Rutherford. Deposit #68   Cindy SoJonathan Sahagun

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## Radioactive Curves and Calculations

Example:
We have entered copper-64 (k = - 0.05331), potassium-42 (k = - 0.05776), and sodium-24 (k = - 0.03850) for 20 hours on the "Graph" menu as our default example.
Click "Graph" to see the result.  Then try the "CalcAge" and "CalcRate" options.

### Please Select the graph or the calculations:

Graph - graphs the radioactive curve based on decay rates.

CalcAge - uses decay rates and amounts to calculate the age.

CalcRate - uses half-times to calculate the decay rate.

Enter maximum time
Enter The decay rate #1
Type
Enter The decay rate #2
Type
Enter The decay rate #3
Type
Calculate by
Enter original amount
Enter remaining amount
Enter the decay rate #1
Enter the decay rate #2
Enter the decay rate #3
The objects age is (decay rate #1)
The objects age is (decay rate #1)
The objects age is (decay rate #1)
Enter the half-life #1
Enter the half-life #2
Enter the half-life #3
The objects age is (decay rate #1)
The objects age is (decay rate #1)
The objects age is (decay rate #1)
days hours
years
 t1/2 = kdays = iodine-125 60 d 0.01155 iodine-131 8 d 0.08664 lutetium-177 6.7 d 0.10345 phosphorus-32 14.3 d 0.04847 rhenium-186 3.8 d 0.18240 strontium-82 25 d 0.02772 strontium-89 50 d 0.01386 xenon-133 5 d 0.13862
 t1/2 = khours = bismuth-213 0.77 h 0.90019 copper-64 13 h 0.05331 Fluoro-deoxy glucose (FDG) 2 h 0.34657 gallium-67 78 h 0.00888 molybdenum-99 66 h 0.01050 potassium-42 12 h 0.05776 sodium-24 18 h 0.03850 technetium-99m 6 h 0.11552 yttrium-90 64 h 0.01083
 t1/2 = kyears = cobalt-60 0.875 y 0.79216 cobalt-57 0.75 y 0.92419 carbon-14 5730 y 0.000121 tritium-3 12.3 y 0.05635

seconds

 t1/2 = kseconds krypton-81 13 s 0.05331

 Half-lives of four common radioisotopes: Experiment by entering data -  the decay rate k  - from above.   Be sure to enter a negative (-) in the rate representing exponential decay. Warning:  Be sure to enter half-lives with the same units of time - all years, days, or hours.  Otherwise comparisons in one graph are obviously not valid.

Background:

 Plot of carbon-14 decay rate against age of the sample in years. Historically known datable points (Ptolemaic period in Egypt) permited researchers to verify the concept of radiocarbon dating. Different radioisotopes have different half-lives.  These range from fractions of a second to billions of years.  However, with few exceptions, the only radioisotopes found in the natural world are those with long half-lives ranging from millions to billions of years.  In 1947 the chemist Willard Frank Libby developed carbon-14 dating techniques leading to his Nobel Prize (1960).  His methods are now found in a variety of situations.   Carbon-14 has a half-life of 5,730 years, which may sound like a large number.  But on the scale of existence of the universe,  this half-life is quite small and thus a convenient yardstick for researchers.  Carbon-14 dating is especially popular with anthropoligists seeking to date the age of bones.  There are many other examples.  Almost every biology lab will have a phosphate counter.  Physicists have studied tritium decay seeking to understand fusion on the Sun.   In the medical sciences, radioisotopes with short half-lives decay so rapidly that detection - imaging - is difficult.  At the same time, the quality of rapid decay may be highly desirable for both diagnosis and therapy, e.g., chemotherapy.  Clearly this is an important research topic.

From math class to data in science and medical labs . . .

Mathematics texts usually treat both exponential growth (bacterial growth, population growth, compound interest)  and exponential decay in the same chapter.  All are logarithmic functions.  But scientists traditionally express rate constants as a positive number - though the rate may represent an exponential decline.  Thus we sometimes find a difference between math texts and science texts in the formula for decay.   Science texts will have a negative ( - ) in the exponent of the formula for exponential decay.
 Derivation: Radioactive decay calculation from the AP* Calculus exam: *AP® Course Descriptions and various test items.  Copyright© 2005 by the College Board. Reproduced with permission.  All rights reserved.  < http://apcentral.collegeboard.com >.

Useful Links and Books

R. Chang,  Physical Chemistry for the Biosciences, University Science Books, 2005, pp. 314-318.
R. E. Dickerson, H. B. Gray, G. P. Haight,  Chemical Principles, W. A. Benjamin, 1970, pp. 503-521.
For a fascinating discussion of where radioisotopes are being using in the medical sciences:
< http://www.uic.com.au/nip26.htm >.
For decay as a function of time:
< http://www.lon-capa.org/~mmp/applist/decay/decay.htm >.
For more general information on radioactive decay:
< http://en.wikipedia.org/wiki/Radioactive_decay >.
 JAVA animation contributed by Cindy So cso133@gmail.com 2006. Javascript Update contributed by Jonathan Sahagun jonathansahagun93@gmail.com 2018.