Radioisotopes, and their
use in “dating” rocks
Radioactive Decay
Certain isotopes of some elements are not
stable. They naturally change (decay) over
time into other elements. For example:
uranium-238 (U-238) decays into
potassium-40 (K-40) decays into
lead-206 (Pb-206)
argon-40 (Ar-40)
carbon-14 (C-14)
nitrogen-14 (N-14)
decays into
Example – decay of uranium-235 into lead-207
Half-life = 700 million years
(one half-life later)
50% remaining
(two half-lives later)
25% remaining
As the parent isotope decreases,
the daughter isotope increases
Daughter isotope percentage
Parent isotope percentage
Many steps in the decay of
Uranium-238 into lead-206
Many steps in the decay of Uranium-238 into lead-206
(another way of looking at it)
Many steps in the decay of Uranium-238 into lead-206
BUT – the first one determines the half-life (in this case)
Symbol
Element
U-238
Uranium-238
Radiation
alpha
Th-234 Thorium-234
beta
Pa-234 Protactinium-234 beta
U-234
Uranium-234
alpha
Th-230 Thorium-230
alpha
Ra-226 Radium-226
alpha
Rn-222 Radon-222
alpha
Po-218 Polonium-218
alpha
Pb-214 Lead-214
beta
Bi-214 Bismuth-214
beta
Po-214 Polonium-214
alpha
Pb-210 Lead-210
beta
Bi-210 Bismuth-210
beta
Po-210 Polonium-210
alpha
Pb-206 Lead-206
none
Half-Life
4.46 billion years
24.1 days
1.17 minutes
247,000 years
80,000 years
1,602 years
3.82 days
3.05 minutes
27 minutes
19.7 minutes
1 microsecond
22.3 years
5.01 days
138.4 days
stable
Decay
Product
Th-234
Pa-234
U-234
Th-230
Ra-226
Rn-222
Po-218
Pb-214
Bi-214
Po-214
Pb-210
Bi-210
Po-210
Pb-206
(none)
SO:
U-238 has a half-life of 704 million years.
Say a sample of a rock contains 800 atoms of the
“parent” isotope (U-238), and only 200 atoms of
the “daughter” isotope (Pb-206).
How old is the rock?
800 atoms of the parent isotope, 200 atoms of the “daughter” isotope
This means that 80% of the parent isotope remains,
so about 0.4 half-lives have passed since the rock
was formed (see the red line).
Percentage of Parent Isotope Remaining
Predicted Decay Rate of an Isotope over Time
100
90
80
70
60
50
40
30
20
10
0
0.4 x 704 million = 281 million years.
0
1
2
3
4
5
6
Number of Half-lives
7
8
9
10
Say a sample of a rock contains 250 atoms of the
“parent” isotope (U-238), and 750 atoms of the
“daughter” isotope (Pb-206).
How old is the rock?
(U-238 half-life =
704 million years)
Percentage of Parent Isotope Remaining
Predicted Decay Rate of an Isotope over Time
100
90
80
70
60
50
40
30
20
10
0
0
1
2
3
4
5
6
Number of Half-lives
7
8
9
10
This means that 25% of the parent isotope remains.
so 2 half-lives have passed since the rock was formed.
2 x 704 million = 1408 million years (1.4 billion yrs)
Percentage of Parent Isotope Remaining
Predicted Decay Rate of an Isotope over Time
100
90
80
70
60
50
40
30
20
10
0
0
1
2
3
4
5
6
Number of Half-lives
7
8
9
10