14. A sample that originally contained 2.5 g of rubidium-87 now contains 1.25 g. The half-life of rubidium-87 is 6 x 10^10 years. How old is the sample? Is this possible? Why or why not?

The age of the sample is . It is possible, since the definition of half-life is the time taken by the isotope to halve its mass.

Explanation:

All radioactive isotopes decays exponentially, the decay is represented by the following formula:

(1)

Where:

- Initial mass of the isotope, measured in grams.

- Current mass of the isotope, measured in grams.

- Time, measured in years.

- Time constant, measured in years.

Now we clear the time of the isotope within the formula:

In addtion, the time constant can be calculated in terms of the half-life (), measured in years:

(2)

If we know that , and , then the age of the isotope is:

The age of the sample is . It is possible, since the definition of half-life is the time taken by the isotope to halve its mass.