• The absolute age is the real age of a rock or fossil in years. It is found using radioactivity.

• Some minerals contain unstable (radioactive) elements such as uranium-238 and carbon-14.
• Their nuclei give off radiation and change into more stable elements.
• A radioactive isotope decays at a constant rate which is characteristic of that element and is not changed by heat, pressure or chemical reactions.
• That makes it a reliable clock.
• Half-life the time required for half the quantity (half the nuclei) of a radioactive element to decay.

• After 1 half-life, 1/2 remains; after 2 half-lives, 1/4 remains; after 3, 1/8; after 4, 1/16; and so on.
• After n half-lives the fraction left is (1/2)ⁿ.
• By measuring how much of the radioactive element remains in the rock and how much of its decay product has formed, scientists can calculate how much time has passed since the rock formed.
• Examples of isotope pairs:

Worked example 3: carbon-14

• A wooden object has only 25% of its original carbon-14. How old is it? (Half-life = 5730 years.)
• 25% = 1/4 = (1/2)², so 2 half-lives have passed. Age = 2 × 5730 = 11 460 years.

Worked example 4: fraction remaining

• How much of a 80 g sample of a radioactive isotope remains after 3 half-lives?
• Fraction = (1/2)³ = 1/8; mass = 80/8 = 10 g. (After the first half-life 40 g; after the second 20 g; after the third 10 g.)

Worked example 5: age of a rock

• A rock contains 12.5% of the original amount of a radioactive isotope whose half-life is 100 million years. How old is the rock?
• 12.5% = 1/8 = (1/2)³, so 3 half-lives have passed. Age = 3 × 100 = 300 million years.
• Reality check any age you calculate for a rock must be less than the age of Earth (about 4.6 billion years). For uranium-238, whose half-life is 4.5 billion years, a rock that formed with Earth would have lost only about half of its uranium.

Worked example 6: the reverse problem

1. A fossil bone is 17 190 years old.
2. How much of its original carbon-14 remains?
3. Number of half-lives = 17 190 ÷ 5730 = 3.
4. Fraction left = (1/2)³ = 1/8 = 12.5%.

• Zircon crystals. Tiny zircon crystals from Jack Hills in Australia are very hard, and they contain uranium that decays into lead; this makes them an accurate "geologic clock".
• Some are about 4.4 billion years old.
• Studies show Earth is about 4.6 billion years old.