If you find an igneous rock which has 450 radioactive isotopes and 3,150 stable daughter isotopes, how many half-lifes of this isotope have passed since this rock first formed?

Explanation:

To find the half-lifes of the isotope we need to use the following equation:

    (1)

where Nt: is the amount of the isotope that has not yet decayed after a time t, N₀: is the initial amount of the isotope, t: is the time and : is the half-lifes.

By solving equation (1) for t we have:

Having that:

Nt = 450

N₀ = 3150 + 450 = 3600,

The half-lifes of the isotope is:

Therefore, 3 half-lives of the isotope passed since the rock was formed.

I hope it helps you!