Question

If an isotope has a half-life of 50 million years and an 1/8 of the sample remaining consists of that isotope, the age of the rock from which it was taken is:

Answer 1

The age of the rock from which the sample was taken is approximately 150 million years, calculated by multiplying the number of half-lives (3) needed to reduce the isotope sample to 1/8 its original amount by the half-life duration (50 million years).

Step-by-step explanation:

If an isotope has a half-life of 50 million years, and 1/8 of the original sample remains, we can determine the age of the rock by considering how many half-lives have passed. After one half-life, half of the original isotope remains (1/2), after two half-lives, a quarter remains (1/4), and this process continues such that after three half-lives, an eighth remains (1/8).

Since each half-life is 50 million years and we need 3 half-lives for the sample to be reduced to 1/8, we multiply the number of half-lives by the length of one half-life:

3 half-lives × 50 million years/half-life = 150 million years

Therefore, the rock is approximately 150 million years old.

Answer 2

150 million years old

Explanation:

If we have an isotope that has a half-life of 50 million years, we need just need to divide the numbers in order to get to one eight of the full number, than multiply it by 50 million in order to get the result.

If one half is 50 million years, than dividing one more half, which will gives one fourth of the total, will brings us to 100 million. Dividing the one fourth by two will leads to the one eight of the full number, and adding 50 million more years, we get 150 million years. So the rock in question has 150 million years of age.