2) If a rock has 70.7% Uranium-235 (parent) to 29.3% Lead-207 (daughter) isotopes, what is the age of that rock

The age of that rock is approximately 353.3 million years.

Explanation:

According to the statement, 29.3 percent of the original mass of Uranium-235 became Lead-207. We know that decay of isotopes is represented by the following ordinary linear differential equation:

(Eq. 1)

Where:

- Rate of change of mass in time, measured in grams per year.

- Current mass of the isotope, measured in grams.

- Time constant, measured in years.

The solution of this differential equation is:

(Eq. 2)

Where:

- Initial mass of the isotope, measured in grams.

- Time, measured in years.

And we solve the expression for time herein:

Besides, time constant can be calculated as a function of half-life. Please notice that half-life of Uranium-235 is 704 million years. The equation is presented below:

(Eq. 3)

Where is the half-life of the isotope, measured in years.

If we know that and , then:

The age of that rock is approximately 353.3 million years.