Samarium-146 has a half-life of 103.5 million years. After 1.035 billion years, how much samarium-146 will remain from a 205-g sample?

1.035 billion years is 10 half-lives, since 1,035 million ÷ 103.5 million = 10. After 10 half-lives, the remaining mass is 205 ÷ 2¹⁰ = 205 ÷ 1,024 ≈ 0.200 g, so the answer is 0.200 g.

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