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Multiple Choice
After two half-lives, what fraction of a radioactive sample remains undecayed?
A
1/2
B
2/3
C
1/8
D
1/4
Verified step by step guidance
1
Understand that a half-life is the time required for half of a radioactive sample to decay.
After one half-life, the fraction of the sample remaining is \(\frac{1}{2}\).
After two half-lives, the fraction remaining is the fraction remaining after the first half-life multiplied by \(\frac{1}{2}\) again, because half of the remaining sample decays each half-life.
Express this mathematically as \(\left( \frac{1}{2} \right)^2\) to represent two successive half-lives.
Calculate the expression to find the fraction remaining after two half-lives, which is \(\frac{1}{4}\).