Question

three half - lives have passed for radioactive isotopes in an igneous rock. the half - life of the isotope million years, how old is the rock?
o 12.5 million years
o 150 million years
o 450 million years
o 87.5 million years

Explanation:

Step1: Recall the relationship between half - lives and age

The age of the rock is the product of the number of half - lives and the half - life of the isotope.

Step2: Identify the number of half - lives and half - life value

The number of half - lives $n = 3$. Let's assume the half - life of the isotope is 150 million years (the value is not given in the problem statement but we need to use one of the options to work backward. If we assume the half - life $t_{1/2}=150$ million years).

Step3: Calculate the age of the rock

The age of the rock $A=n\times t_{1/2}$. Substituting $n = 3$ and $t_{1/2}=150$ million years, we get $A=3\times150 = 450$ million years.

Answer:

C. 450 million years