Question

A rock is going to be analyzed for its radioactive isotope contents, X and Y. X is the parent and Y is the daughter isotope. Assume that the half-life of the radioactive isotopes is 5,730 years. Based on this information, answer the following two questions. A) How much of the parent (X) and how much of the daughter (Y) were present at the time the rock formed? Choose one of the following and explain why . A) X = 100 % ; Y = 100 % B) X = 0 % ; Y = 100 % C) X = 100 % ; Y = 0 % D) X = 50 % ; Y = 50 % B) How much of the parent (X) and how much of the daughter (Y) will be present after 5,730 years? Choose one of the following and explain why.
A) X = 75 % ; Y = 25 %
B) X = 50 % ; Y = 50 %
C) X = 25 % ; Y = 75 %
D) X = 12.5 % ; Y = 87.5%

Answer 1

Answer:

C) X=100%; Y=0%

B) X=50%; Y=50%

Explanation:

The oldest rocks on Earth are about four billion years old. When a rock forms, it contains unstable isotope and no daughter isotopes, so every rock will contain 100% parent isotope and 0% daughter isotope.

The half-life of the radioactive isotope Of this particular rock is 5730 years. The half-life is an amount of time needed for half of the parent isotope (50%) to become a daughter isotope. In this case, after 5730 years, half of the initial parent isotope will transform to daughter isotope, which means that after 5730 years, there will be 50-50 of the parent and daughter istotopes presented in the rock. After two half-lives, there will be only 25% of the parent isotope remaining (that’s half of the previous 50% which remained after first half-life), and after three half-lives, there will be only 12,5% of the parent isotope remaining and so on.