Question

1/4 of a sample of thorium-232 remains. How long has the sample been decaying?

A) 30 years
B) 20 years
C) 10 years
D) 40 years

Answer 1

The sample has been decaying for approximately 600 years.

Step-by-step explanation:

We can determine the time it takes for a sample to decay by using the concept of half-life. In this case, 1/4 of the sample remains, which means the remaining amount is equal to 25% of the original amount. Since it takes one half-life for the sample to decay by half, we can calculate the number of half-lives by repeatedly dividing 25% by 2 until we reach 1. Starting with 100%, we have 25%, 12.5%, 6.25%. It takes 3 half-lives for the sample to decay to 1/4, which is approximately 600 years (200 years per half-life). Therefore, the sample has been decaying for approximately 600 years.