80.5k views
4 votes
A geologic sample is found that contains 1,800 uranium-235 atoms and 5,400 lead-207 atoms. How old is this sample?

a) 1.5 billion years
b) 2.0 billion years
c) 2.5 billion years
d) 3.0 billion years

1 Answer

4 votes

Final answer:

The geologic sample, containing uranium-235 and lead-207, is approximately 1.5 billion years old, determined through the principles of radioactive dating and the known half-life of uranium-235.

Step-by-step explanation:

The age of a geologic sample can be determined by using the principles of radioactive dating. To calculate the age of the sample that contains 1,800 uranium-235 (U-235) atoms and 5,400 lead-207 (Pb-207) atoms, we must use the known half-life of U-235, which is approximately 0.704 billion years (Gyr). Since the ratio of U-235 to Pb-207 in the sample is 1:3, it indicates that two half-lives have passed, because the number of lead atoms is three times the number of uranium atoms. One half-life would reduce the uranium atoms to half their original number and create an equal amount of lead atoms. Two half-lives would reduce the remaining uranium atoms by another half, and the number of lead atoms would then triple the number of uranium atoms present. Thus, since one half-life is 0.704 Gyr, two half-lives would be 0.704 Gyr x 2 = 1.408 Gyr, which we can round to approximately 1.5 billion years. Therefore, the answer is a) 1.5 billion years.

User Tagyro
by
8.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories