Radioactive Decay
 An
unstable atomic nucleus
emits a form of radiation
(alpha, beta, or gamma) to
become stable.
 In other words, the nucleus
decays into a different atom.
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

Atoms that are radioactive have nuclei that
spontaneously decompose to form a different
nuclei and produce one or more particles
These particles can be any of the following



Alpha particle (42He)
Beta particle (0-1e)
Gamma particle (00γ)


Atoms that are radioactive have a
neutron/proton ratio much greater than 1
Radioactivity can be detected by a Geiger
counter


Medicine – radioactive materials are used as
tracers in the body
Energy sources – energy can be obtained
through two nuclear processes


Fission: a nucleus divides into smaller fragments
Fusion: nuclei combine to form a larger nucleus

The measurement of the time
required for a radioactive material to
decay is called its half-life.

This is the time required for half of the
nuclides in a sample to decay.
 Half-life of 238U is 4.5 billion years
 Half-life of 131I is 8.07 days
 Half-life of 194Po is 0.7 second

25
As an example, Technetium-99 has a half-life of
6 hours.This means that, if there is 100 grams of
Technetium is present initially, after six hours,
only 50 grams of it would be left.After another
6 hours, 25 grams, one quarter of the initial
amount will be left. And that goes on like this.


Now lets try to solve a half-life calculation
problem…
Sodium-24 has a half-life of 15 hours. How
much sodium-24 will remain in an 18.0 g
sample after 60 hours?

Initially, Sodium -24 is 18 grams, and after 15
hours, I will have ½ of it left. 60 hours is four
half lives The arrows represent the half-life.
18 g
9g
4.5g
2.25
It goes like this till it reaches ____ grams, in 60
1/2
1/2
1/2
1/2
hours
 You
have 400 mg of a
radioisotope with a half-life of
5 minutes. How much will be
left after 30 minutes?
14
 Suppose
you have a 100 mg
sample of Au-191, which has
a half-life of 3.4 hours. How
much will remain after 10.2
hours?
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
Cobalt-60 is a radioactive
isotope used in cancer
treatment. Co-60 has a half-life
of 5 years. If a hospital starts
with a 1000 mg supply, how
many mg will need to be
purchased after 10 years to
replenish the original supply?
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Half-Life Calculation #1
 6.25 mg
 Half-Life Calculation #2
 12.5 mg
 Half-Life Calculation #3
 750 mg

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



We have some radioactive
materials in our bodies.
One of the isotopes is
carbon-14.
Carbon-14 is an isotope of
the carbon in CO2.
All living things take it in
during respiration.

Scientist use carbon-14 to date very
old things.





Decayed carbon-14 is continually being
replaced in the body.
Once the organism dies the carbon-14 is no
longer replaced, but what is there continues to
decay.
By examining the amount of carbon-14 left in
the material, scientist can estimate the age of
the subject.
The half life of carbon-14 is 5730 years
Accurate to about 20,000-50,000 years.
1) A fossilized tree killed by a volcano was
studied. It had 6.25 percent of the amount of
carbon-14 found in a sample of the same size
from a tree that is alive today. When did the
volcanic eruption take place?
You need to find out how many times ½ (0.5)
must be used as a factor to produce 0.0625.
The answer is 4 times because
0.5 X 0.5 X 0.5 X 0.5 = 0.0625
4 half-lives have gone by and each half-life is 5730
years.
5730 years X 4 = 22,920 years
2) A rock was analyzed using potassium-40. The
half-life of potassium-40 is 1.25 billion years. If
the rock had only 25 percent of the potassium40 that would be found in a similar rock
formed today, calculate how long ago the rock
was formed.
Potassium-40 Half-life is 1.25 billion years
2) Convert 25% to a decimal --- 0.25
0.5 X 0.5 = 0.25
2 half-lives have gone by.
1.25 billion X 2 = 2.50 billion years
3) Ash from an early fire pit was found to have
12.5 percent as much carbon-14 as would be
found in a similar sample of ash today. How
long ago was the ash formed?
Convert 12.5% to a decimal ---
0.125
0.5 X 0.5 X 0.5 = 0.125
3 half-lives have gone by.
5730 X 3 = 17,190 years ago
4) A rock sample has 12.5% of the potassium-40
that would be present in a similar rock formed
today. How old is the rock sample?
Convert 12.5% to a decimal ---
0.5 X 0.5 X 0.5 = 0.125
0.125
3 half-lives have gone by.
1.25 billion X 3 = 3.75 billion years old
5) How old is a piece of wood in which the
carbon-14 is 3.12% of that in wood formed
today?
Convert 3.12% to a decimal --- 0.0312
0.5 X 0.5 X 0.5 X 0.5 X 0.5 = 0.03125
5 half-lives have gone by.
5730 X 5 = 28,650 years old

Amount remaining = amount of original
sample
2n
n = number of half-lives
1)
An isotope of cesium (cesium-137) has a halflife of 30 years. If 1.0 mg of cesium-137
disintegrates over a period of 90 years, how
many mg of cesium-137 would remain?
Amount remaining =
amount1.0
of original
mg
sample
23n
1 half life = 30 years
Therefore, 90 years is equal to how many half lives?
n=3
4. Sodium-25 was to be used in an experiment,
but it took 3.0 minutes to get the sodium from the
reactor to the laboratory. If 5.0 mg of sodium-25
was removed from the reactor, how many mg of
sodium-25 were placed in the reaction vessel 3.0
minutes later if the half-life of sodium-25 is 60
seconds?
amount of original sample
Amount remaining
5.0 mg =
2n3
1 half life = 60 seconds
Therefore, 3 minutes is equal to how many half lives?
n=3