Question

You are dating Moon rocks based on their proportions of uranium-238 (half-life of about 4.5 billion years) and its ultimate decay product, lead.

1.Find the age for a rock for which you determine that 58% of the original uranium-238 remains, while the other 42% has decayed into lead.
T=( ) billion years
2.Find the age for a rock for which you determine that 66% of the original uranium-238 remains, while the other 34% has decayed into lead.
T=( ) billion years

Answer 1

In radioactive dating, the age of a rock can be determined by comparing the amount of U-238 to the amount of Pb-206. For the first question, if 58% of the original U-238 remains, the rock's age is approximately 4.5 billion years. For the second question, if 66% of the original U-238 remains, the rock's age is approximately 9 billion years.

Step-by-step explanation:

In radioactive dating, the age of a rock can be determined by comparing the amount of U-238 to the amount of Pb-206 in the rock sample. Since U-238 has a half-life of about 4.5 billion years, we can use this information to calculate the age of the rock.

For the first question, if 58% of the original U-238 remains, then 42% has decayed into Pb-206. This means that one half-life has passed. So, the age of the rock is approximately 4.5 billion years.

Similarly, for the second question, if 66% of the original U-238 remains, then 34% has decayed into Pb-206. This indicates that two half-lives have passed. So, the age of the rock is approximately 9 billion years.

Answer 2

1) The rock is 3.78 billion years old.

2) The rock is 3.06 billion years old.

Step-by-step explanation:

Hi there!

The half-life is the time at which half of a substance in a sample disappears. In this case, half of the uranium of the rocks will disappear in 4.5 billion years.

1) 42% of the uranium has disappeared. Then, if 50% disappears in 4.5 billion years, 42% has disappeared in (42% · 4.5 billion years/50%) 3.78 billion years. Then the rock is 3.78 billion years old.

2) The procedure is the same as above: if 50% of uranium will disappear in 4.5 billion years, 34% has disappeared in (34% · 4.5 billion years/50%) 3.06 billion years. Then, the rock is 3.06 billion years old.

Have a nice day!