1. Half-Life

2. Half-Life 20 g 10 g 5 g 2.5 g after 1 half-life after 2 half-lives
Start
Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 757

3. Half-Life g I Xe b- 1.00 mg 0.875 mg 0.500 mg 0.750 mg Xe 0.500 mg I I
b emissions
g emissions
89.9%
7.3%
131 53 I 54 Xe
Xe*
Half-Life
1.00 mg
0.875 mg
0.500 mg
0.750 mg
131 54 Xe
131 53
0.500 mg I
131 53 I
0.250 mg
0.125 mg
8.02 days
16.04 days
24.06 days
0.00 days I
131 53 Xe 54 b- -1 + g
Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 757

4. Half-life of Radiation
Initial amount
of radioisotope
Number of half-lives
Radioisotope remaining (%)
100 50 25
12.5
After 1 half-life
After 2 half-lives
After 3 half-lives
t1/2
t1/2
t1/2

5. Half-Life Plot Half-life of iodine-131 is 8 days20
Half-life of iodine-131 is 8 days 15
1 half-life
Amount of Iodine-131 (g) 10 16
2 half-lives 5 24
3 half-lives 32
4 half-lives
etc… 40 48 56 8
Time (days)
Timberlake, Chemistry 7th Edition, page 104

6. Half-Life of Isotopes
Half-Life and Radiation of Some Naturally Occurring Radioisotopes
Isotope Half-Live Radiation emitted
Carbon-14
5.73 x 103 years b
Potassium-40
1.25 x 109 years
b, g
Radon-222
3.8 days a
Radium-226
1.6 x 103 years
a, g
Thorium-230
7.54 x 104 years
a, g
Thorium-234
24.1 days
b, g
Uranium-235
7.0 x 108 years
a, g
Uranium-238
4.46 x 109 years a

7. Half-life (t½)
Time required for half the atoms of a radioactive nuclide to decay.
Shorter half-life = less stable.
1/2
1/4
1/8
1/16
1/1
1/2
1/4
1/8
1/16
Ratio of Remaining Potassium-40 Atoms
to Original Potassium-40 Atoms
1 half-life
1.3
1 half-lives
2.6
3 half-lives
3.9
5.2
Time (billions of years)
Newly formed
rock
Potassium
Argon
Calcium

8. Half-life (t½)
Time required for half the atoms of a radioactive nuclide to decay.
Shorter half-life = less stable.
1/1
Newly formed
rock
Potassium
Argon
Calcium
Ratio of Remaining Potassium-40 Atoms
to Original Potassium-40 Atoms
1/2
1/4
1/8
1/16
1 half-life
1.3
1 half-lives
2.6
3 half-lives
3.9
1 half-lives
5.2
Time (billions of years)

9. Copyright © Pearson Education, Inc., publishing as Benjamin Cummings

10. How Much Remains? After one half-life, of the original atoms remain.1 2
After two half-lives, ½ x ½ = 1/(22) = of the original atoms remain. 1 4
After three half-life, ½ x ½ x ½ = 1/(23) = of the original atoms remain. 1 8
After four half-life, ½ x ½ x ½ x ½ = 1/(24) = of the original atoms remain. 1 16
After five half-life, ½ x ½ x ½ x ½ x ½ = 1/(25) = of the original atoms remain. 1 32
After six half-life, ½ x ½ x ½ x ½ x ½ x ½ = 1/(26) = of the original atoms remain. 1 64
Accumulating
“daughter”
isotopes 1 2 1 4
Surviving
“parent”
isotopes 1 8 1 16 1 32 1 64 1
128
Beginning
1 half-life
2 half-lives
3 half-lives
4 half-life
5 half-lives
6 half-lives
7 half-lives

11. 2. The burning creates carbon dioxide gas comprised of carbon-12
1. A small piece of
fossil is burned in
a special furnace.
2. The burning creates carbon
dioxide gas comprised of carbon-12
isotopes and carbon-14 isotopes.
Stable
C-12 isotope
Nitrogen
Decaying
C-14 isotope
3. As the carbon-
14 decays into
nitrogen-14, it
emits an electron.
Electron
All organisms absorb, use and accumulate the element carbon during life. There are several types or isotopes, depending upon the number of neutrons in the carbon atom. It is the difference in the behavior of these isotopes that permits researchers to estimate age.
While alive, organisms accumulate both carbon-12 and carbon-14 isotopes at a steady ratio of about 12 trillion C-12 isotopes to each C-14 isotope. Carbon-12 is a stable isotope. It doesn't change or decay. A fossil or piece of parchment contains as much C-12 as the original living dinosaur or goat.
In contrast, C-14 is radioactive. It is always in a process of decay, with a half-life of 5,730 years. That means that after 5,730 years, only half of the original C-14 in an organic sample will remain, the rest having decayed into another element, specifically nitrogen-14.
By measuring the ratio of C-12 to remaining C-14 atoms in a sample and comparing it to the known rate of C-14 decay, researchers can estimate the age of almost any organic object.
4. A radiation
counter records
the number of
electrons emitted.
Note: Not to scale.
SOURCE: Collaboration for NDT Education MATT PERRY / Union-Tribune

12. The iodine-131 nuclide has a half-life of 8 days
The iodine-131 nuclide has a half-life of 8 days. If you originally have a
625-g sample, after 2 months you will have approximately?
40 g
20 g
10 g
5 g
less than 1 g
Data Table: Half-life Decay
~ Amount Time # Half-Life
625 g
312 g
156 g
78 g
39 g
20 g
10 g
5 g
2.5 g
1.25 g
0 d
8 d
16 d
24 d
32 d
40 d
48 d
56 d
64 d
72 d 1 2 3 4 5 6 7 8 9
N = No(1/2)n
N = amount remaining
No = original amount
n = # of half-life(s)
N = (625 g)(1/2)7.5
Assume 30 days = 1 month
N = g
60 days
= 7.5 half-life(s)
8 days

13. N ln = - k t No 0.693 ln 2 t1/2 = k 0.693 k 1.5 g k = 1.209 x 10-4
Given that the half-life of carbon-14 is 5730 years, consider a sample of fossilized wood that, when alive, would have contained 24 g of carbon-14. It now contains 1.5 g of carbon-14.
How old is the sample?
Data Table: Half-life Decay
ln = - k t N No
Amount Time # Half-Life
24 g
12 g
6 g
3 g
1.5 g
0 y
5,730 y
11,460 y
17,190 y
22,920 y 1 2 3 4
0.693
ln 2
t1/2 = k
0.693
Petrified wood is a type of fossil: it exists of fossil wood where all the organic materials have been replaced with minerals (most often a silicate, such as quartz), while retaining the original structure of the wood.
5730 y = k
ln = - (1.209x10-4) t
1.5 g
24 g
k = x 10-4
t = 22,933 years

14. Half-Life Practice Calculations
The half-life of carbon-14 is 5730 years. If a sample originally contained 3.36 g of C-14, how much is present after 22,920 years?
Gold-191 has a half-life of 12.4 hours. After one day and 13.2 hours, 10.6 g of gold-19 remains in a sample. How much gold-191 was originally present in the sample?
There are 3.29 g of iodine-126 remaining in a sample originally containing 26.3 g of iodine The half-life of iodine-126 is 13 days. How old is the sample?
A sample that originally contained 2.5 g of rubidium-87 now contains 1.25 g. The half-life of rubidium-87 is 6 x 1010 years. How old is the sample? Is this possible? Why or why not?
0.21 g C-14
84.8 g Au-191
39 days old
6 x 1010 years
(60,000,000,000 billions years old)
What is the age of Earth???
Demo: Try to cut a string in half seven times (if it begins your arms length).

15. 3.36 g of C-14, how much is present after 22,920 years?
The half-life of carbon-14 is 5730 years. If a sample originally contained
3.36 g of C-14, how much is present after 22,920 years?
Data Table: Half-life Decay
t1/2 = years
Amount Time # Half-Life
3.36 g
1.68 g
0.84 g
0.42 g
0.21 g
0 y
5,730 y
11,460 y
17,190 y
22,920 y 1 2 3 4
22,930 years
n =
5,730 years
n = 4 half-life
Australian scientists have found a new species of hobbit-sized humans who lived about 18,000 years ago on an Indonesian island.
The discovery adds another piece to the complex puzzle of human evolution.
The partial skeleton of Homo floresiensis, found in a cave on the island of Flores, is of an adult female that was a meter tall, had a chimpanzee-sized brain and was substantially different from modern humans.
It shared the isolated island to the east of Java with miniature elephants and Komodo dragons.
The hominins walked upright and probably evolved into their dwarf size because of environmental conditions and coexisted with modern humans in the region for thousands of years.
(# of half-life)(half-life) = age of sample
(4 half-life)(5730 years) = age of sample
22,920 years

16. Half-life
Half-life worksheet