Uses for Nuclear Material
Half-Life


is the
required for
of a radioisotope’s nuclei to decay into its products.
For any radioisotope,
# of ½ lives
% Remaining
0
1
2
3
100%
50%
25%
12.5%
4
5
6
6.25%
3.125%
1.5625%
Half-Life
Half-Life
100
90
80
% Remaining
70
60
50
40
30
20
10
0
0
1
2
3
# of Half-Lives
4
5
6
7
Half-Life


For example, suppose you have 10.0 grams of
strontium – 90, which has a half life of 29 years.
How much will be remaining after x number of
# of ½ lives
Time (Years)
Amount
years?
Remaining (g)
You can use a table:
0
1
2
3
4
0
29
58
87
116
10
5
2.5
1.25
0.625
Half-Life

Or an equation!
Half-Life

Example 1: If gallium – 68 has a half-life of 68.3
minutes, how much of a 160.0 mg sample is left
after 1 half life? 2 half lives? 3 half lives?
mt = m0* (.5)n
mt = 160mg * (.5)1 mt = 160mg * (.5)2 mt = 160mg * (.5)3
mt = 80mg
mt = 40mg
mt = 20mg
Half-Life

Example 2: Cobalt – 60, with a half-life of 5 years,
is used in cancer radiation treatments. If a hospital
purchases a supply of 30.0 g, how much would be
left after 15 years?
n = total time/half-life
n = 15/5 = 3
mt = m0* (.5)n
mt = 30g * (.5)3
mt = 3.75g
Half-Life

Example 3: The half-life of polonium-218 is 3.0
minutes. If you start with 20.0 g, how long will it
take before only 1.25 g remains?
mt = m0* (.5)n
1.25 = 20g * (.5)n
0.0625 = (.5)n
ln(0.0625) = ln((.5)n)
ln(0.0625) = n*ln(.5)
4= n
4*3mins =12 mins
Half-Life

Example 4: A sample initially contains 150.0 mg of
radon-222. After 11.4 days, the sample contains
22.75 mg of radon-222. Calculate the half-life.
mt = m0* (.5)n
22.75 = 150g * (.5)n
0.152 = (.5)n
ln(0.152) = ln((.5)n)
ln(0.152) = n*ln(.5)
2.72= n
n = total time/half-life
2.72 = 11.4/half-life
half-life = 11.4/2.72
half-life = 4.19 days
Uses of Radiation

Medical applications
 Radiation
of cancer cells
 Radioactive tracers to detect disease
 Sterilization of equipment


Commercial products (smoke alarms)
Radioactive dating
Radiation therapy


High doses of
radiation can causes
the normal functioning
of living cells to
mutate and leads to
abnormal growth and
eventually cancer.
VERY HIGH doses will
kill cells – especially
fast-growing ones like
cancer cells
Gamma ray treatment
Radioactive Tracers in Diagnosis


Used to follow the flow of
a substance through the
body.
Pattern of colors/locations
can tell doctors how well
particular organs are
functioning.
 Technetium-99 is one
of the most common –
used extensively in
imaging
 Iodine-131 for
thyroid function
 Thalium-201 for
cardiac problems
 Flourine-18 for PET
scans
Sterilisation



Sterilisation - Killing
microorganisms on
medical instruments
using a strongly ionising
source of radiation.
Used on medical
instruments while they
are still within their
packaging.
Food can also be
irradiated to increase
shelf-life.
Sterile syringe within its
packaging
Commercial products: Smoke detectors

A radioactive source
inside the alarm ionises
an air gap so that it
conducts electricity –
americium-241, an
alpha emitter


Very long half-life
In a fire, smoke
prevents the radiation
and therefore a drop in
electric current which
sets off the alarm.
Radioactive Dating

Radiocarbon dating: the ages of specimens of
organic origin can be estimated by measuring the
amount of cabon-14 in a sample.
Radiocarbon dating
Living material (for example a plant) contains a known tiny
proportion of radioactive carbon-14. This isotope is produced
when high speed neutrons (part of cosmic radiation) collide
with nitrogen gas in our atmosphere.
14
7
N +
1
0
14
n
6
C +
1
1
p
When organisms die, they no longer have a constant
proportion of carbon-14. It decays by beta emission back to
the stable nitrogen-14 with a half-life of about 5600 years.
14
6
C
14
7
N
+
0
-1
β
-
Calculating ages

Example: A piece of wood taken from a cave dwelling in New
Mexico is found to have a carbon-14 activity (per gram of
carbon) only 0.636 times that of wood today. Estimate the
age of the wood. (The half-life of carbon-14 is 5730 years.)
mt = m0* (.5)n
0.636 = 1 * (.5)n
0.636 = (.5)n
ln(0.636) = ln((.5)n)
ln(0.636) = n*ln(.5)
0.65= n
0.65*5730 = 3741.1 yrs
Limitations of radiocarbon dating



The dating process assumes that the level of cosmic
radiation reaching the Earth is constant – corrected by using
known ages of objects, esp trees (tree rings)
Radiocarbon dating is limited to reasonably young samples
no older than ~50,000 years because the amount of
carbon-14 becomes to small to measure accurately
Rocks and other very old objects are dated using
isotopes with significantly longer half-lives.
Potassium-40 decays to argon-40: half-life = 1.25 billion
years
 Uranium-238 decays to lead-206: half-life = 4.47 billion
years
