If a radioactive isotope in a rock has a half-life of 10000 years and the ratio of radioactive parent to stable daughter is 1 to 3 how old is the rock?

Answer 1

At the time the rock is created, the radioactive isotope is present in that rock in a ratio of 1 to zero with regard to the stable daughter. After one half-life, which is 10,000 years, the isotope to daughter ratio is 1 to 1. After another half-life, which is another 10,000 years, the ratio is 1 to 3. The rock is 20,000 years old.

To see it another way, after the first half-life is complete, half the material is the original isotope, and half is the daughter. That's a 1 to 1 ratio. After another half-life (another 10,000 years) has passed, half the original isotope that was left has become the daughter. That's one quarter more of the daughter that will be added to the quantity of the daughter existing after the first half-life. That means that one quarter of the original isotope will be left after 2 half-lives, and the rest (the other 3/4ths of the material) will be the daughter. The ratio of the original isotope to the daughter after 2 half-lives (20,000 years) is 1 to 3.

Answer 2

Given the 1:3 parent-daughter ratio at time t and knowing the half-life of the isotope is 10000 years, we can calculate the age of the rock to be approximately 20000 years. This is because after one half-life, half of the parent isotope would decay to form the stable daughter isotope, resulting in the 1:3 ratio becoming 1:1.

Answer 3

300,000 years old

Answer 4

The rock is 2 millions years old.