Transcript Radioactive Decay

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 doesn’t matter how
much you start with. After 1 half-life, half of it will have decayed.
Each element has it’s 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. It’s like a clock
keeping perfect time.
Now let’s see how we can use half-life to determine the
age of a rock or other artifact.
The grid below represents a quantity of C14. Each time you click,
one half-life goes by. Try it!
Ratio of
Half
% C14
%N14
14
14
C to N
C – blue
N - red
lives
14
0
100%
0%
no ratio
As we begin notice that no time
has gone by and that 100% of the
material is C14
Age = 0 half lives (5700 x 0 = 0 yrs)
14
The grid below represents a quantity of C14. Each time you click,
one half-life goes by. Try it!
Ratio of
Half
% C14
%N14
14
14
C to N
C – blue
N - red
lives
14
14
0
100%
0%
no ratio
1
50%
50%
1:1
After 1 half-life (5700 years), 50% of
the C14 has decayed into N14. The ratio
of C14 to N14 is 1:1. There are equal
amounts of the 2 elements.
Age = 1 half lives (5700 x 1 = 5700 yrs)
The grid below represents a quantity of C14. Each time you click,
one half-life goes by. Try it!
Ratio of
Half
% C14
%N14
14
14
C to N
C – blue
N - red
lives
14
Age = 2 half lives (5700 x 2 = 11,400 yrs)
14
0
100%
0%
no ratio
1
50%
50%
1:1
2
25%
75%
1:3
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 C:N ratio. It
will be useful later.
The grid below represents a quantity of C14. Each time you click,
one half-life goes by. Try it!
Ratio of
Half
% C14
%N14
14
14
C to N
C – blue
N - red
lives
14
Age = 3 half lives (5700 x 3 = 17,100 yrs)
14
0
100%
0%
no ratio
1
50%
50%
1:1
2
25%
75%
1:3
3
12.5%
87.5%
1:7
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, 1:7
C14 – blue
N14 - red
In the example above, the ratio is 1:3.
How can we find the age of a
sample without knowing how
much C14 was in it to begin
with?
1) Send the sample to a lab which
will determine the C14 : N14
ratio.
2) Use the ratio to determine how
many half lives have gone by
since the sample formed.
Remember, 1:1 ratio = 1 half life
1:3 ratio = 2 half lives
1:7 ratio = 3 half lives
3) Look up the half life on page 1 of your reference tables and multiply that
that value times the number of half lives determined by the ratio.
If the sample has a ratio of 1:3 that means it is 2 half lives old. If the half
life of C14 is 5,700 years then the sample is 2 x 5,700 or 11,400 years old.
C14 has a short half life and can only be used on organic material.
To date an ancient 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 U:Pb ratio in the rock today. This
can be obtained by standard laboratory techniques.
Rock Sample
As you can see the U:Pb ratio is 1:1. From what
we saw earlier a 1:1 ratio means that 1 half life
has passed.
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.
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 = 1:1 ratio
2 HL = 1:3
3 HL = 1:7
4 HL = 1:15
If you said that the sample was
8,000 years old, you understand
radioactive dating.
If you’re unsure and want an
explanation just click.
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 X:Y 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
1:15 ratio.
2) As seen in the list on the previous slide, 4 half-lives must go by in
order to reach a 1:15 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.
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.
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.
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?