Question

1. a rock layer contains a radioactive element that originally had 100 grams of the parent isotope. after 3 half - lives, only 12.5 grams of the parent isotope remain. based on this information, what is the most likely half - life of the element if the rock is 6 million years old? 3 million years 1 million years 2 million years 1.5 million years

Explanation:

Step1: Recall half - life formula relationship

The number of half - lives $n$ can be related to the age of the rock $t$ and the half - life $T_{1/2}$ by $t = nT_{1/2}$.

Step2: Determine number of half - lives

We know from the problem that the amount of parent isotope has gone through 3 half - lives to get from 100 grams to 12.5 grams.

Step3: Calculate half - life

We are given that $t = 6$ million years and $n = 3$. Using the formula $T_{1/2}=\frac{t}{n}$, we substitute the values: $T_{1/2}=\frac{6}{3}=2$ million years.

Answer:

2 million years