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

Deposit #68

Cindy So Jonathan Sahagun

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.

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}

t_{1/2}
=

k_{days} =

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

t_{1/2}
=

k_{hours} =

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

t_{1/2}
=

k_{years} =

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}

t_{1/2}
=

k_{seconds}

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: