How Old is the Moon Rock?

Calculation of the Age of the Moon Rock

A sample of moon rock was found to contain 40 argon-40 atoms for every 5 potassium-40 atoms. The half-life of postassium-40 is 1.25 billion years. Assuming no loss of daughter isotopes, how old is the moon rock?

a) 3.75 billion years old

b) 2.5 billion years old

c) 10.5 billion years old

d) 6.75 billion years old

Half life is the time needed for a radioactive molecule to decay 50% or half of its weight. When decay, half of the radioactive parent molecule will be changed into children molecule. So, the ratio of parent: child molecule can be used to determine how many half-lives already happen. The parent molecule would be potassium-40 and the child molecule is argon-40.

The number of half-life would be:
parent molecule/child molecule = (1/2)^(half-life)
5/40= (1/2)^(half-life)
1/8= (1/2)^(half-life)
(1/2)^3=(1/2)^(half-life)
half life= 3

If the half-life is 1.25 billion years, the age of the rock would be:
age= half-life count * half-life duration
age= 3 * 1.25 billion years
age= 3.75 billion years

What is the age of the moon rock based on the given information?

The age of the moon rock based on the given information is 3.75 billion years old.