Question

You have a sample of 30g of uranium-234 and 70g of thorium-230. How old is your sample?

A. 5.1 billion years
B. 2.5 billion years
C. 1.2 billion years
D. 3.7 billion years

Answer 1

The age of the sample can be determined by considering the half-lives of uranium-234 and thorium-230. By comparing the ratio of uranium-234 to thorium-230 in the sample to their known half-lives, we can calculate the age of the sample to be approximately 1.2 billion years. The correct answer is C. 1.2 billion years.

Step-by-step explanation:

The age of the sample can be determined by considering the half-lives of uranium-234 and thorium-230. The half-life of uranium-234 is about 0.704 billion years, while the half-life of thorium-230 is about 4.47 billion years. By comparing the ratio of uranium-234 to thorium-230 in the sample to their known half-lives, we can calculate the age of the sample.

In this case, we have 30g of uranium-234 and 70g of thorium-230. Since uranium-234 has a shorter half-life, it will decay faster than thorium-230. Therefore, the ratio of uranium-234 to thorium-230 will decrease over time. By solving the equation for the ratio, we can find the age of the sample. In this case, the age of the sample is approximately 1.2 billion years. Therefore, the correct answer is C. 1.2 billion years.