Transcript Half-Life
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