Question

A sample contains 6.25 percent parent isotope and 93.75 percent daughter isotopes. If the half-life of the parent isotope is 58 years, how old is the sample?

Answer 1

Answer is: the sample is 232 years old.

Take 100 atoms:

After first half-life: 50% · 100 ÷ 100% = 50.  

After second half-life: 0.5 · 50 = 25.  

After third half-life: 0.5 · 25 = 12.5.  

After fourth half-life: 0.5 · 12.5 = 6.25.

6.25 ÷ 100 · 100% = 6.25%.

4 half-lives will it take before only about 6.25% of the original sample remains.

t = 4 · 58 y.

t = 232 y.

Answer 2

The parent isotope percent will change from 100% to 50% to 25% to 12.5% and to 6.25%. So the sample go through four times of half-life. So the sample is 58*4=232 years old.