Suppose you find a rock that contains 10 micrograms of radioactive potassium-40,which has a half-life of 1.25 billion years.By measuring the amount of its decay product (argon-40)present in the rock,you conclude that there must have been 80 micrograms of potassium-40 when the rock solidified.How old is the rock?
A)1.25 billion years
B)2.5 billion years
C)3.75 billion years
D)5.0 billion years

Question

Quizplus · Accepted Answer

The ratio of the remaining potassium-40 to the initial amount must be:

(remaining amount) / (initial amount) = (decay factor)^(number of half-lives)

where the decay factor is 1/2, since half the potassium-40 decays in each half-life.

Solving for the number of half-lives gives:

(number of half-lives) = log[(remaining amount) / (initial amount)] / log(decay factor)
= log[(10 micrograms) / (80 micrograms)] / log(1/2)
= log(1/8) / (-log(2))
= 3.0

Therefore, the age of the rock is:

(age) = (number of half-lives) x (half-life)
= 3.0 x (1.25 billion years)
= 3.75 billion years

So, the best choice is C, which represents an age of 3.75 billion years.

Suppose You Find a Rock That Contains 10 Micrograms of Radioactive