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)2)6 billion years
B)1)3 billion years
C)3)9 billion years
D)5)2 billion years
E)none of the above

Question

Quizplus · Accepted Answer

The ratio of argon-40 to potassium-40 in the rock indicates that 35 grams of potassium-40 have decayed (40 grams - 5 grams). Since the half-life of potassium-40 is 1.3 billion years, we can use the equation N=N₀(1/2)^(t/t₁/₂) to solve for the age of the rock. Using the values given, we have 35 grams = 40 grams (1/2)^(t/1.3 billion years), which simplifies to 0.875 = (1/2)^(t/1.3 billion years). Taking the logarithm of both sides, we get log(0.875) = (t/1.3 billion years) log(1/2), which gives us t = 9 billion years.

Suppose You Find a Rock That Contains Some Potassium- 40