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Which of the following best describes the half-life of a radioactive isotope?
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15. Chemical Kinetics
Half-Life
Multiple Choice
If a radioactive sample is in its second half-life, what percentage of the original sample remains undecayed (stable) at this point?
A
12.5%
B
75%
C
25%
D
50%
검증된 단계별 안내1
Recall that the concept of a half-life refers to the time required for half of a radioactive sample to decay.
After one half-life, 50% of the original sample remains undecayed.
After the second half-life, half of the remaining 50% will decay, so the remaining amount is half of 50%.
Express this mathematically as \(\left( \frac{1}{2} \right)^2 = \frac{1}{4}\), which represents the fraction of the original sample remaining.
Convert this fraction to a percentage by multiplying by 100%, resulting in 25% of the original sample remaining undecayed after two half-lives.
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