66.7k views
4 votes
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

4 votes

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.

User Patrick Gidich
by
7.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.