Carbon-11 has a half-life of 20.334 minutes. Starting from a 1000 g sample, about how much remains after exactly one hour (about three half-lives)?
A62.5 g
B125 g
C129 g
D250 g
Answer & Solution
Correct answer: C. 129 g
1. One hour is 60 minutes, and 60 divided by 20.334 minutes is close to, but not exactly, 3 half-lives.
2. Halving three times exactly would leave 1000 g divided by 8, or 125 g.
3. Because 60 minutes is slightly less than three full half-lives of 20.334 minutes each, a little more than 125 g remains.
4. Careful calculation using N = N0 times e to the power of minus lambda t gives about 129 g.
5. 62.5 g would need four half-lives, and 250 g is the amount left after only two half-lives.
6. So 129 g is correct, just above the 125 g estimate from three clean halvings.
_Source: OpenStax Physics (CC BY 4.0), Ch 22 "The Atom", section 22.3 Half Life and Radiometric Dating_
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