1. Half Life and Radioactive Decay

2. Nuclear Decay Series All elements above Atomic Number 83 have
Unstable nuclei and are therefore radioactive.
Alpha Particle
Most abundant isotope

3. Thorium Decay Of course Thorium’s atomic number is also
greater than 83. So it to is Radioactive and
Goes through beta decay.
234Pa e 91 -1
Protactinium

4. U-238 Decay Series Protactinium decays Next and so on until
we reach a stable
Non-radioactive
Isotope of lead
Pb-206
Atomic No. 82

5. U-238 Decay Series

6. Decay Series U-238 IS NOT the only radioactive isotope that
Has a specific decay series.
All radioisotopes have specific decay paths
they follow to ultimately reach stability

7. Decay Series Time Span The next Question you might consider asking
is how long does this decay process take?
The half life of U-238 is about 4.5 billion
years which is around the age of the
earth so only about half of the uranium
Initially present when the earth formed has Decayed to date.
Which leads us into a discussion of Nuclear Half life

8. Nuclear Half-life Unstable nuclei emit either an alpha, beta
or positron particles to try to shed mass or
improve their stability.
But can we predict when a nucleus will
Disintegrate?
The answer is NO for individual nuclei
But YES if we look at large #’s of atoms.

9. 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

10. Nuclear Half-life The Half life of any nuclide is independent of:
Temperature, Pressure
or Amount of material left

11. Beanium decay What does the graph of radioactive decay look like?
64 beans
32 beans
16 beans
8 beans
4 beans
Successive half cycles 1 2 3 4
50%
This is an EXPONENTIAL
DECAY CURVE

12. Loss of mass due to Decay
Amount of beanium
Fraction left 1 ½ ¼ 1/8 1/16
Half life’s
If each half life took 2 minutes then 4
half lives would take 8 min.
The equation for the Number of half
Lives is equal to:
Time (elapsed) / Time (half Life)
32 minutes / 4 minutes = 8 half life’s

13. Carbon 14 is a radionuclide used to date
22,920/5730 =
4 Half-life’s t0
Carbon 14 is a radionuclide used to date
Once living archeological finds
Carbon–14 Half-life = 5730 years

14. Half-Lives 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
100
40 grams 1 50
1620 yrs
20 grams 2 25
3240 ? 3
12.5
4860 4
6.25
6480 5
3.125
8100
10 grams
5 grams
2.5 grams
1.25 grams

15. Problem:
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: Half lives = T (elapsed) / T half life = 24/8 = 3
Step 2: 16g (starting amount) g
Half lives

16. Problem:
What is the original amount of a sample of H– 3 if after 36.8years 2.0g are left ?
Table N tells us that the half life of H-3 is yrs.
36.8 yrs / yrs = 3 half lives.
Now lets work backward
Half life 3 2 grams
Half life 2 4 grams
Half life 1 8 grams
Time zero 16 grams

17. Problem:
How many ½ life periods have passed if a sample has decayed to 1/16 of its original amount?
Time zero 1x original amount
First half life ½ original amount
Second half life ¼ original amount
Third half life 1/8
Fourth half life /16

18. Problem:
What is the ½ life of a sample if after 40 years 25 grams of an original 400 gram sample is left ?
Step 2:
Elapsed time = # HL
Half-life
40 years = 4 HL
Half life = 10 years
Step 1:
25 grams 4 half lives
50 3 half lives
100 g 2 half lives
200 g 1 half life
400 g time zero