Wednesday, November 4th, 2015
The blue grid below represents a quantity of C14. Each time you click,
one half-life goes by and turns red.
Ratio of
Half
% C14
%N14
C to N
C14 – blue
N14 - red
lives
14
0
100%
0%
14
no ratio
As we begin notice that no
time has gone by and that
100% of the material 2is C14
The grid below represents a quantity of C14. Each time you click,
one half-life goes by and you see red.
Ratio of
Half
% C14
%N14
C to N
C14 – blue
N14 - red
lives
14
14
0
100%
0%
no ratio
1
50%
50%
1:1
After 1 half-life (5730 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. 3
The blue grid below represents a quantity of C14. Each time you click,
one half-life goes by and you see red .
Ratio of
Half
% C14
%N14
C to N
C14 – blue
N14 - red
lives
14
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 11,460 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
4
will be useful later.
The blue grid below represents a quantity of C14. Each time you click,
one half-life goes by and you see red.
Ratio of
Half
% C14
%N14
C to N
C14 – blue
N14 - red
lives
14
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 (17,190 years) only
12.5% of the original C14 remains. For
each half-life period half of the material
present decays. And again, notice
the
5
ratio, 1:7
6
What is the half life
represented in this
graph?
7
Nuclear Half-life
Every statistically large group of radioactive
nuclei decays at a predictable rate.
This is called the half-life of the nuclide
Half life is the time it takes for half (50%) of the
Radioactive nuclei to decay to the daughter
Nuclide
Beanium decay
What does the graph of radioactive decay look like?
64 beans
Successive half cycles
50%
1
32 beans
2
This is an EXPONENTIAL
DECAY CURVE
16 beans
3
4
8 beans
4 beans
Loss of mass due to Decay
Amount
Fraction left
Half life’s
64
1
32
½
1
16
¼
2
8
4
1/8 1/16
3
4
If each half life took 2 minutes then 4 half lives
would take 8 min.
The equation for the No. of half lives is equal to:
T (elapsed – total) / T (one half Life)
32 minutes / 4 minutes = 8 half life’s
• In order to solve these half problems a table
like the one below is useful.
• For instance, If we have 40 grams of an
original sample of Ra-226 how much is left
after 8100 years?
½ life period
% original
remaining
Time
Elapsed
Amount left
0
100
0
1
50
1620 yrs
40 grams
20 grams
2
25
3240
3
12.5
4860
4
6.25
6480
? 10 grams
? 5 grams
? 2.5 grams
5
3.125
8100
? 1.25 grams
Problem 1:
A sample of Iodine-131 had an original
mass of 16g. How much will remain
in 24 days if the half life is 8 days?
Step 1: How many half lives?
Half life= T (elapsed) / T half life = 24/8 = 3
Step 2: 16g (starting amount)  8  4  2g
Problem 2:
• What is the original amount of a sample of
H–3 if after 36.8 years 2.0g are left if the half
life of H-3 is 12.26 years?
36.8 yrs / 12.26 yrs = 3 half lives.
___  ___  ___  2 g
Half life
3
Half life
2
Half life
1
Time zero
2 grams
4 grams
8 grams
16 grams
Work backwards!
Problem 3:
• How many half life periods have passed if a
sample has decayed to 1/16 of its original
amount?
Time zero
First half life
Second half life
Third half life
Fourth half life
1x original amount
½ original amount
¼ original amount
1/8
1/16
Problem 4:
• What is the ½ life of a sample if after 40
years 25 grams of an original 400 gram
sample is left ?
Step 1:
400  200  100  50  25
4 half lives
Step 2:
Elapsed time = # HL
Half-life
40 years = 4 HL
Half-life
Half life = 10 years
For each problem you need to identify
1. Number of half-lives
2. Starting amount (%, fraction, g, etc.)
3. Ending amount
4. Length of one half-life
5. Total amount of time to get from
starting amount to ending amount
Wednesday, November 4th, 2015
What are the particles?
• Alpha
• Beta
• Gamma
• Positron
Examples – What goes where?!
• Sodium-23 undergoes
beta decay
• Carbon-14 undergoes
electron capture.
• A radioactive isotope
goes through alpha
decay to produce
Nitrogen-14.
• Magnesium-24 is
produced from the
positron emission of an
unstable isotope.
• The beta decay of
Uranium-235 produces
a gamma particle as
well.
Sodium-23 undergoes beta decay
•
Carbon-14 undergoes electron capture.
•
A radioactive isotope goes through
alpha decay to produce Nitrogen-14.
•
Magnesium-24 is produced from the
positron emission of an unstable isotope.
•
The beta decay of Uranium-235
produces a gamma particle as well.
•
For each problem you need to identify
1. The reactant(s) 2. The product(s)
3. Total mass on the left of the arrow
4. Total mass on the right of the arrow
5. Total atomic number on the left of the
arrow
6. Total atomic number on the right of the
arrow