The diagram below illustrates the radioactive decay of Potassium (⁴⁰K), which has a half-life of 1.3 billion years. If a lunar rock is found that currently contains 5 grams of ⁴⁰K, and it is determined that the sample contained 20 grams when it was formed, how old is the lunar rock?

Question

Quizplus · Accepted Answer

We can use the formula for radioactive decay: 
amount remaining = initial amount x (1/2)^(t/half-life) 
where t is the time passed and half-life = 1.3 billion years.

We can plug in the given information: 
5 grams = 20 grams x (1/2)^(t/1.3 billion)

Divide both sides by 20 grams: 
1/4 = (1/2)^(t/1.3 billion)

Take the logarithm of both sides: 
log(1/4) = (t/1.3 billion) x log(1/2)

Simplify: 
log(1/4) = -2 
log(1/2) = -1

Therefore: 
-2 = (t/1.3 billion) x (-1) 
t/1.3 billion = 2 
t = 2 x 1.3 billion = 2.6 billion

Therefore, the lunar rock is 2.6 billion years old.

The Diagram Below Illustrates the Radioactive Decay of Potassium (40K)

The Diagram Below Illustrates the Radioactive Decay of Potassium (⁴⁰K)