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 concept

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

Step2: Identify number of half - lives and age of rock

We know from the problem that the number of half - lives $n = 3$ (since the amount of parent isotope has gone through 3 half - life periods) and the age of the rock $t=6$ million years.

Step3: Solve for half - life

Using the formula $t = nT_{1/2}$, we can re - arrange it to $T_{1/2}=\frac{t}{n}$. Substituting $t = 6$ million years and $n = 3$ into the formula, we get $T_{1/2}=\frac{6}{3}=2$ million years.

Answer:

2 million years