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The radioactive element carbon-14 decays to half its size approximately every 5700 years. Determine the remaining mass of 20 g of carbon-14 after 34,200 years. What is the remaining mass? (Round to the nearest tenth and include the unit)

A) 1.2 g
B) 2.5 g
C) 5.0 g
D) 10.0 g

1 Answer

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Final answer:

After 34,200 years, which accounts for 6 half-lives of carbon-14, a starting mass of 20 g would decay to approximately 0.3 g, upon rounding to the nearest tenth. This result does not match the provided options, suggesting a possible mistake in the options or calculations.

Step-by-step explanation:

The radioactive element carbon-14 decays to half its size approximately every 5700 years. To determine the remaining mass of 20 g of carbon-14 after 34,200 years, you would divide the number of years by the half-life to find out how many half-lives have passed. In this case, 34,200 ÷ 5700 equals exactly 6 half-lives. Starting with 20 grams, after the first half-life you'd have 10 grams, then 5 grams, and so on.

After six half-lives, the mass is halved six times: 20 g → 10 g → 5 g → 2.5 g → 1.25 g → 0.625 g → 0.3125 g. Rounding to the nearest tenth, the remaining mass is 0.3 g. However, this answer does not match any of the given options A) 1.2 g B) 2.5 g C) 5.0 g D) 10.0 g, indicating there might have been a mistake in the calculation or in the provided options.

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