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Cindy So

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Radioactivity discovered in 1896 by French scientist Henri Becquerel
and extensively investigated by Marie Curie, Pierre Curie and Ernest Rutherford.

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Version 1.5.0 required.


This section features . . .

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.


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:
Table of half-lives
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.
Half-life equations

Background:

Plot of carbon-14 decay rate against age of the sample in years.
Carbon-14 decay rate plot
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:

Derivation of equations
Radioactive decay calculation from the AP* Calculus exam:

Sample AP Calculus problem
*AP® Course Descriptions and various test items.  Copyright© 2005 by the College Board.
Reproduced with permission.  All rights reserved.  < http://apcentral.collegeboard.com >.

Stamp Useful Links and Books
Curie stamp
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 >.
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JAVA  animation contributed by

Cindy So
cso133@gmail.com

2006.