A radioactive nucleus has a half-life of 3 years. After 9 years, what fraction of the original sample remains?

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Multiple Choice

A radioactive nucleus has a half-life of 3 years. After 9 years, what fraction of the original sample remains?

Explanation:
Half-life behavior means the amount remaining is halved every half-life. With a 3-year half-life, after 9 years three half-lives have passed (9 ÷ 3 = 3). After each half-life, the fraction left is multiplied by 1/2: 1/2 after the first, 1/4 after the second, and 1/8 after the third. So the original sample remaining is 1/8.

Half-life behavior means the amount remaining is halved every half-life. With a 3-year half-life, after 9 years three half-lives have passed (9 ÷ 3 = 3). After each half-life, the fraction left is multiplied by 1/2: 1/2 after the first, 1/4 after the second, and 1/8 after the third. So the original sample remaining is 1/8.

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