U-238 has a half-life of 4.5 billion years and a present day abundance of 99.3%.U-235 has a half-life of 0.7 billion years and a present day abundance of 0.7%.Assuming a steady rate of decay,how long ago did these two isotopes have the same abundance?

Question

Quizplus · Accepted Answer

Let x be the age in billions of years when the two isotopes had the same abundance.

At that time, the abundance of U-238 would have decayed to 0.703% (its present-day abundance of 99.3% reduced by a factor of 2^(x/4.5)).

At the same time, the abundance of U-235 would have decayed to 99.297% (its present-day abundance of 0.7% increased by a factor of 2^(x/0.7)).

Setting these equal we get:

0.703 = 99.297 * 2^(x/0.7- x/4.5)

Solving this equation gives x = 5.9 billion years.

Therefore, the answer is (C).

U-238 Has a Half-Life of 4