Question

Thorium-229 is the radioactive substance that gives lantern mantels their eerie glow. The half life of thorium-229 is 7340 years.

If one mantel consists of 0.25 grams of thorium, how much thorium will remain after 14,680 years?
Responses
A 0.0625g0.0625g
B 0.125g0.125g
C 0.25g0.25g
D 1.0g

Answer 1

To determine how much thorium-229 remains after 14,680 years, we can use the concept of half-lives.

The half-life of thorium-229 is 7340 years. After each half-life, the quantity of the substance is reduced by half.

First, we calculate how many half-lives fit into 14,680 years:

\[
\text{Number of half-lives} = \frac{14,680 \text{ years}}{7340 \text{ years/half-life}} \approx 2
\]

Now that we know that 14,680 years is approximately 2 half-lives, we can calculate the remaining amount of thorium:

Starting amount: 0.25 grams

After the first half-life (7340 years):
\[
0.25 \, \text{g} \div 2 = 0.125 \, \text{g}
\]

After the second half-life (14,680 years):
\[
0.125 \, \text{g} \div 2 = 0.0625 \, \text{g}
\]

Therefore, after 14,680 years, 0.0625 grams of thorium-229 will remain.

The correct response is:
**A 0.0625g**