Question

Assume you are given a sample of material and asked to determine its age. You the measure isotopes in the rock and determine that it has 125 mg of Radium-228 (the parent isotope) and 875 mg of Actinium-229 (the daughter isotope). How old is the rock sample if Radium-228 has a half life of 5.75 years?

Answer 1

To determine the age of the rock sample, calculate the number of half-lives that have occurred for Radium-228. The rock is approximately 8.6 months old.

Step-by-step explanation:

To determine the age of the rock sample, we need to calculate the number of half-lives that have occurred for the Radium-228 isotope. Since the half-life of Radium-228 is 5.75 years, we can use the formula:

Age = Number of Half-Lives × Half-Life

First, we calculate the number of half-lives:

Number of Half-Lives = (Initial Amount of Radium-228) / (Amount of Radium-228 Remaining)

Number of Half-Lives = 125 mg / (125 mg + 875 mg) = 125 mg / 1000 mg = 0.125

Now we can calculate the age:

Age = 0.125 × 5.75 years = 0.7188 years = 8.6 months

Therefore, the rock sample is approximately 8.6 months old.