Question

If a rock had 1,000 grams of a radioisotope at time 0, and its half-life is 150,000 years, how old would a rock sample be that has only 125 grams of the original parent isotope left?

Answer 1

To find the age of a rock sample with 125 grams of a radioisotope that had an original amount of 1,000 grams, calculate the number of half-lives it takes to reach 125 grams from 1,000 grams.

Step-by-step explanation:

The question involves calculating the age of a rock sample based on the remaining amount of a radioisotope and its half-life. We are given that the original amount of the radioisotope was 1,000 grams and the half-life is 150,000 years. The sample now has 125 grams of the isotope left.

To calculate the age, we can use the concept that in each half-life, the amount of the radioisotope remaining is reduced to half its previous amount. We can calculate the number of half-lives that have passed to reduce the radioisotope from 1,000 grams to 125 grams.

• After the first half-life, the amount of isotope would be halved (1000 g / 2 = 500 g).
• After the second half-life, it would be halved again (500 g / 2 = 250 g).
• After the third half-life, it would be halved once more (250 g / 2 = 125 g).

Since each half-life is 150,000 years and it took 3 half-lives to get from 1,000 grams to 125 grams, the rock sample would be 450,000 years old (3 half-lives x 150,000 years per half-life).