Astr 138 Assignment #6 - Due Thurs Oct 27, 2005
Age of Moon Rocks by Radiometric Dating
Parent Isotope Daughter Isotope Half-life
Thorium-232 Lead-208 14 billion years
Uranium-238 Lead-206 4.47 billion years
Potassium-40 Argon-40 1.25 billion years
Uranium-235 Lead-207 704 million years
Carbon-14 Nitrogen-14 5,730 years
A radioactive substance is one that is unstable. It will eventually decay to a simpler form. The rate at which a radioactive
substance decays is described by its half-life. The half-life is the amount of time that must pass before half of the original
radioactive substance has decayed away.
The table above shows a few radioactive substances (the “parent”), what stable form they can decay to (the “daughter”),
and how long the half-life is. Note that there are several intermediate stages between each parent-daughter pair.
For example, imagine that you have a 1 gram rock of potassium-40 in it. After 1.25 billion years (i.e., one half-life) there
will be 0.5 grams remaining. After 2.5 billion years (two half-lives) there will be 0.25 grams left. After 3.75 billion years
(three half-lives) there will be 0.125 grams left. The rest of the rock will be daughter products.
We describe this situation mathematically by:
current amount
original amount =1
2t/thalf (1)
where tis the elapsed time since the rock formed, and thalf is the half-life of the parent, given in the table. The fraction
current amount/original amount is a number between 0 and 1. If only 10% of a parent remains, then this fraction
equals 0.10.
Imagine that you are analyzing Moon rocks returned by the Apollo missions. You detect small amounts of uranium-238
and its lead daughter product.
1. In a ro ck from the lunar highlands, you determine that 55% of the original uranium-238 remains, the other 45% has
decayed. What is the age of this rock?
2. In a ro ck from the lunar lowlands, you determine that 63% of the original uranium-238 remains. What is the age of
this rock?
3. Which ro ck is older, highland or lowland? How do your results compare with the density of craters in the highlands
versus the lowlands? Are your age results surprising, or expected?
