you have found a volcanic rock with uranium - 235. it has 25% of the parent isotope (u - 235). half - life…

Explanation:

Step1: Understand the concept of half - life

The amount of a radioactive isotope decreases by half every half - life. If the initial amount of the parent isotope is $N_0$ and the remaining amount is $N$, and the number of half - lives passed is $n$, then $N = N_0\times(\frac{1}{2})^n$. Here, $N = 0.25N_0$.

Step2: Solve for the number of half - lives

Set up the equation $0.25N_0=N_0\times(\frac{1}{2})^n$. Divide both sides by $N_0$ (since $N_0\neq0$), we get $0.25 = (\frac{1}{2})^n$. Since $0.25=\frac{1}{4}=(\frac{1}{2})^2$, then $n = 2$.

Step3: Calculate the age of the rock

The half - life of U - 235 is $T_{1/2}=710$ million years. The age of the rock $t=n\times T_{1/2}$. Substitute $n = 2$ and $T_{1/2}=710$ million years into the formula, we get $t=2\times710$ million years $ = 1420$ million years. Since 1 billion = 1000 million, 1420 million years = 1.420 billion years.

Answer:

1.420 billion years old