Radioactive Decay

1
Radioactive Decay
Radioactive elements are unstable. They decay,
change, into different elements over time. Here
are some facts to remember
The half-life of an element is the time it takes
for half of the material you started with to
decay. Remember, it doesnt matter how much you
start with. After 1 half-life, half of it will
have decayed.
Each element has its own half-life ( page 1 of
your reference table)
Each element decays into a new element (see page
1) C14 decays into N14 while U238 decays into
Pb206 (lead), etc.
The half-life of each element is constant. Its
like a clock keeping perfect time.
Now lets see how we can use half-life to
determine the age of a rock or other artifact.
2
The grid below represents a quantity of C14. Each
time you click, one half-life goes by. Try it!
C14 blue N14 - red
As we begin notice that no time has gone by and
that 100 of the material is C14
3
The grid below represents a quantity of C14. Each
time you click, one half-life goes by. Try it!
C14 blue N14 - red
After 1 half-life (5700 years), 50 of the C14
has decayed into N14. The ratio of C14 to N14 is
11. There are equal amounts of the 2 elements.
4
The grid below represents a quantity of C14. Each
time you click, one half-life goes by. Try it!
C14 blue N14 - red
Now 2 half-lives have gone by for a total of
11,400 years. Half of the C14 that was present at
the end of half-life 1 has now decayed to N14.
Notice the CN ratio. It will be useful later.
5
The grid below represents a quantity of C14. Each
time you click, one half-life goes by. Try it!
C14 blue N14 - red
After 3 half-lives (17,100 years) only 12.5 of
the original C14 remains. For each half-life
period half of the material present decays. And
again, notice the ratio, 17
6
So how can this knowledge be used to determine
the age of an ancient artifact such as a rock? To
date a rock we use the uranium lead method
(U238 Pb206).
Here is our sample. Remember we have no idea how
much U238 was in the rock originally but all we
need is the UPb ratio in the rock today.
This can be obtained by standard laboratory
techniques.
As you can see the UPb ratio is 11. From
what we saw earlier a 11 ratio means that 1 half
life has passed.
Rock Sample
Now all we have to do is see what the half-life
for U238 is. We can find that information on
page 1 of the reference tables.
1 half-life 4.5 x 109 years (4.5 billion), so
the rock is 4.5 billion years old.
Try the next one on your own.............or to
review the previous frames click here.
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Element X (Blue) decays into Element Y (red) The
half life of element X is 2000 years. How old is
our sample?
See if this helps 1 HL 11 ratio 2 HL 13 3
HL 17 4 HL 115
If you said that the sample was 8,000 years old,
you understand radioactive dating. If youre
unsure and want an explanation just click.
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Element X (blue) Element Y (red) How old is our
sample?
We know that the sample was originally 100
element X. There are three questions First What
is the XY ratio now? Second How many half-lives
had to go by to reach this ratio? Third How many
years does this number of half-lives represent?

1) There is 1 blue square and 15 red squares.
Count them. This is a 115 ratio.
2) As seen in the list on the previous slide, 4
half-lives must go by in order to reach a
115 ratio.
3) Since the half life of element X is 2,000
years, four half-lives would be 4 x 2,000
or 8,000 years. This is the age of the sample.
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Regents question may involve graphs like this
one. The most common questions are "What is the
half-life of this element?"
Just remember that at the end of one half-life,
50 of the element will remain. Find 50 on the
vertical axis, Follow the blue line over to the
red curve and drop straight down to find the
answer
The half-life of this element is 1 million years.
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Another common question is "What percent of the
material originally present will remain after 2
million years?"
Find 2 million years on the bottom, horizontal
axis. Then follow the green line up to the red
curve. Go to the left and find the answer.
After 2 million years 25 of the original
material will remain.
11
End Notes
Carbon 14 can only be used to date things that
were once alive. This includes wood, articles of
clothing made from animal skins, wool or cotton
cloth, charcoal from an ancient hearth. But
because the half-life of carbon 14 is relatively
short the technique would be useless if the
sample was extremely (millions of years) old.
There would be too little C14 remaining to
measure accurately. The other isotopes mentioned
in the reference tables, K40, U238, and Rb87 are
all used to date rocks. These elements have very
long half-lives. The half-life of U238 for
example is the same as the age of the earth
itself. That means that half the uranium
originally present when the earth formed has now
decayed. The half life of Rb87 is even
longer. Lastly, when you see a radioactive decay
question ask yourself What is the ratio? How
many half-lives went by to reach this ratio?
How many years do those half-lives represent?