Answer :

Final answer:

The final mass of a 94g sample of lead-210 after 91.2 years, given its half-life of 22.3 years, would be less than 1g. None of the options provided (23.5 g, 47 g, 70.5 g, 94 g) are correct.

Explanation:

To answer your question about the final mass of the 94g sample of lead-210 after 91.2 years, we need to understand the concept of half-life, which is a term used in nuclear physics and chemistry to represent the time required for half the atoms in a radioactive sample to decay.

Lead-210 is a radioactive isotope with a half-life of 22.3 years. This implies that after every 22.3 years, approximately half of the lead-210 present at the beginning of the time period will have decayed.

Given that the time period stated in the question is 91.2 years, we can calculate the number of half-lives by doing the following: 91.2 ÷ 22.3 ≈ 4. This implies that approximately 4 half-lives have passed during this time.

After the first half-life, the 94g sample would reduce to half, giving us 47g. After the second half-life, the remaining 47g would halve again to 23.5g. On repeating the process for the 3rd and 4th half-lives, we would be left with a mass that is less than 1g.

Thus, none of the choices provided in the question (23.5 g, 47 g, 70.5 g, 94 g) would represent the final mass of the sample of lead-210 after 91.2 years.

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