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 55% of the original uranium-238 remains, while the other 45% has decayed into lead.

2. Find the age for a rock for which you determine that 68% of the original uranium-238 remains, while the other 32% has decayed into lead.

Answer 1

In radioactive dating, the age of rocks can be estimated by comparing the proportion of remaining uranium-238 to lead-206. If 55% of uranium-238 remains, the rock is approximately 4.5 billion years old. If 68% of uranium-238 remains, the rock is approximately 9 billion years old.

Step-by-step explanation:

In radioactive dating, the decay of uranium-238 into lead is used to determine the age of rocks. The half-life of uranium-238 is approximately 4.5 billion years. By comparing the proportion of uranium-238 remaining to the amount of lead-206 in a rock sample, the age of the rock can be estimated.

For the first example, if 55% of the original uranium-238 remains, it means 45% has decayed into lead. This indicates that one half-life has passed, so the rock is approximately 4.5 billion years old.

For the second example, if 68% of the original uranium-238 remains, it means 32% has decayed into lead. This corresponds to approximately two half-lives, so the rock is approximately 9 billion years old.

Answer 2

1. Use the formula:


`-kt = ln[(FinalAmount)/(InitialAmount)]`


`k = ln2 / half-life`

So,
`t = - (4.5)/(ln2) * ln[(0.55)/(1)]`

t = 3.8 billion yr

2. Same formula:


`t = - (4.5)/(ln2) * ln[(0.63)/(1)]`

t = 2.93 billion yr.