This section features . . .
Radioactive Curves and Calculations
Example:
We
have entered copper64 (k =  0.05331), potassium42 (k =  0.05776),
and sodium24 (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}


t_{1/2}
=

k_{days} =

iodine125 
60 d

0.01155

iodine131

8 d

0.08664

lutetium177

6.7 d

0.10345

phosphorus32

14.3 d

0.04847

rhenium186

3.8 d

0.18240

strontium82 
25 d

0.02772

strontium89 
50 d

0.01386

xenon133

5 d

0.13862



t_{1/2}
= 
k_{hours} =

bismuth213

0.77 h

0.90019

copper64

13 h

0.05331

Fluorodeoxy glucose
(FDG) 
2 h

0.34657

gallium67 
78 h

0.00888

molybdenum99 
66 h

0.01050

potassium42

12 h

0.05776

sodium24

18 h

0.03850

technetium99m 
6 h

0.11552

yttrium90 
64 h

0.01083



t_{1/2}
= 
k_{years} =

cobalt60

0.875 y

0.79216

cobalt57

0.75 y

0.92419

carbon14

5730 y

0.000121

tritium3

12.3 y

0.05635




_{
seconds}

t_{1/2}
= 
k_{seconds}

krypton81

13 s

0.05331





Halflives 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 halflives with the same units of time  all years, days,
or hours. Otherwise comparisons in one graph are obviously not
valid.


Background:
Plot of carbon14 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 halflives. 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 halflives ranging from millions to billions of years.
In 1947 the chemist Willard Frank Libby developed carbon14 dating
techniques leading to his Nobel Prize (1960). His methods are now
found in a variety of situations. Carbon14 has a halflife
of 5,730 years, which may sound like a large number. But on the
scale of existence of the universe, this halflife is quite small
and thus a convenient yardstick for researchers. Carbon14 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 halflives 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. 314318. 
R. E. Dickerson, H. B.
Gray, G. P.
Haight, Chemical Principles,
W. A. Benjamin, 1970, pp. 503521.

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.loncapa.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.


