Suppose you find a rock that contains some potassium-40 (half-life of 1.3 billion years).You measure the amount and determine that there are 5 grams of potassium-40 in the rock.By measuring the amount of its decay product (argon-40)present in the rock,you realize that there must have been 40 grams of potassium-40 when the rock solidified.How old is the rock?
A)1.3 billion years
B)2.6 billion years
C)3.9 billion years
D)5.2 billion years
E)none of the above

Question

Quizplus · Accepted Answer

The half-life of potassium-40 is 1.3 billion years, which means that every 1.3 billion years, half of the potassium-40 in the rock will decay into argon-40. 
If there are currently 5 grams of potassium-40 in the rock, and there were 40 grams when the rock solidified, then 35 grams of potassium-40 must have decayed (40-5=35). 
Since each half-life is 1.3 billion years, and there have been three half-lives (since 0.5^3 = 0.125, meaning 12.5% of the original amount of potassium-40 is left), the rock must be 3.9 billion years old. 
Therefore, the answer is C.

Suppose You Find a Rock That Contains Some Potassium-40 (Half-Life