1. Radioactive Decay Now, let’s see how we can use the half-life rate to
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 ( ESRT page).
Each element decays into a new element (ESRT page 1)
C14 decays into N14 while U238 decays into Pb206 (lead), etc.
The half-life of each element is constant.
Now, let’s see how we can use the half-life rate to
determine the age of a rock or other object.

2. The grid below represents a quantity of C14. Each time you click,
one half-life goes by. Try it!
C14 – blue N14 - red
Half
lives
% C14
%N14
Ratio of
C14 to N14
100% 0%
no ratio
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
Half
lives
% C14
%N14
Ratio of
C14 to N14
100% 0%
no ratio 1
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.

4. The grid below represents a quantity of C14. Each time you click,
one half-life goes by. Try it!
C14 – blue N14 - red
Half
lives
% C14
%N14
Ratio of
C14 to N14
100% 0%
no ratio 1
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.

5. The grid below represents a quantity of C14. Each time you click,
one half-life goes by. Try it!
C14 – blue N14 - red
Half
lives
% C14
%N14
Ratio of
C14 to N14
100% 0%
no ratio 1
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.

6. Try the next one on your own.............or
So, how can this knowledge be used to determine the age of an
ancient object 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 U:Pb ratio in the rock today. This
can be obtained by standard laboratory techniques.
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.
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 Earth Science 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.

7. 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.

8. 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.

9. The half-life of this element is 1 million years.
Regents question may involve
graphs like this one. The most
common Regents question is:
"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.

10. After 2 million years 25% of the original material will remain.
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. radioactive substance
Half of the radioactive substance breaks down during each half life.
25%
100%
of the original
radioactive substance
50%
12.5%
6.25%
3.125%

12. Lastly, when you see a radioactive decay question
SUMMARY:
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 ES 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 these three questions:
> What is the ratio?
> How many half-lives went by to reach this ratio?
> How many years do those half-lives represent?