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Carbon-14 has a half-life of 5,730 years. The sample weighs 120 grams.a. How many years would it take for % of the original amount of carbon-14 in the sample to decay?b. After five half-lives, how many grams of carbon-14 would remain?

a. How many years would it take for 25% of the original amount of carbon-14 in the sample to decay?
A) 5730 years
B) 11460 years
C) 17190 years
D) 22920 years
b. After five half-lives, how many grams of carbon-14 would remain?
A) 3.75 grams
B) 7.5 grams
C) 15 grams
D) 30 grams

2. The half-life of Pa-234 is 6.75 hours. How much (what fraction) of a sample of this isotope remains after 20-25 hours?

1 Answer

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Final answer:

Carbon-14 has a half-life of 5,730 years. It would take 11,460 years for 25% of the original amount of carbon-14 in the sample to decay. After five half-lives, 7.5 grams of carbon-14 would remain.

Step-by-step explanation:

(a) To determine how many years it would take for % of the original amount of carbon-14 in the sample to decay, we can use the concept of half-life. The half-life of carbon-14 is 5,730 years. After each half-life, the amount of carbon-14 remaining is halved. So, if we want to determine how many years it would take for 25% of the original amount to decay, we can calculate the number of half-lives required.

Since 50% is remaining after the first half-life, then 25% should remain after the second half-life. This means it would take two half-lives or 2 x 5,730 = 11,460 years for 25% of the original amount to decay. Therefore, the answer is B) 11,460 years.

(b) After five half-lives, the amount of carbon-14 remaining can be calculated by repeatedly halving the sample size. The equation for calculating the remaining amount after n half-lives is given by:

Remaining amount = Initial amount x (1/2)^n.

For five half-lives, we plug in n = 5 and the initial amount of 120 grams to calculate the remaining amount:

Remaining amount = 120 grams x (1/2)^5 = 7.5 grams.

Therefore, the answer is B) 7.5 grams.

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