²¹⁰Pb has a half-life of 22.3 years and decays to produce ²⁰⁶Hg. If you start with 7.50 g of ²¹⁰Pb, how many grams of ²⁰⁶Hg will you have after 17.5 years?

Question

Quizplus · Accepted Answer

The half-life of ²¹⁰Pb is 22.3 years, which means that after 17.5 years, ²¹⁰Pb will have decayed by a factor of 2^17.5/22.3 = 2^0.785 = 2.19. Therefore, the amount of ²¹⁰Pb remaining after 17.5 years will be 7.50 g / 2.19 = 3.42 g. Since ²¹⁰Pb decays to produce ²⁰⁶Hg, the amount of ²⁰⁶Hg produced after 17.5 years will be 7.50 g - 3.42 g = 4.08 g.

210Pb Has a Half-Life of 22

²¹⁰Pb Has a Half-Life of 22