Uranium-238 undergoes radioactive decay with a half-life of 4.5 billion years,producing lead-206.After 13.5 billion years,what is the ratio of uranium-238 to lead-206 in a sample that originally contained only uranium-238?
A) 1:2
B) 1:3
C) 1:4
D) 1:8

Question

Quizplus · Accepted Answer

After 4.5 billion years, half of the uranium-238 would have decayed into lead-206. After another 4.5 billion years, half of the remaining uranium-238 would decay, leaving 25% uranium-238 and 75% lead-206. After another 4.5 billion years, half of the remaining uranium-238 would decay again, leaving 12.5% uranium-238 and 87.5% lead-206. Finally, after a total of 13.5 billion years, we have gone through three half-lives, so the ratio of uranium-238 to lead-206 is 1:7. Therefore, the correct answer is D, which has a 1:8 ratio.

Uranium-238 Undergoes Radioactive Decay with a Half-Life of 4