A rock sample contains 1/8 micrograms of the parent radioactive isotope Aluminum-26 and 7/8 micrograms of its daughter isotope Magnesium-40. If the half-life of this decay is approximately 700,000 years, how old is this rock?

Question

Quizplus · Accepted Answer

The amount of parent isotope remaining after time t is given by:N(t) = N(0) * (1/2)^(t/t1/2)where N(0) is the initial amount of parent isotope, t1/2 is the half-life, and t is the time elapsed.In this case, N(0) = 1/8 micrograms, t1/2 = 700,000 years, and N(t) = 7/8 micrograms. Solving for t, we get:t = t1/2 * log2(N(0)/N(t))= 700,000 years * log2(1/8 / 7/8)= 700,000 years * log2(1/7)= 2.1 million yearsTherefore, the rock is 2.1 million years old.

A Rock Sample Contains 1/8 Micrograms of the Parent Radioactive