The half-life of carbon-14 is 5715 years. How long would it take for 100 grams to decay to 12.5 grams

We are given:

half-life of carbon = 5715 years

Initial mass = 100 grams

Final mass = 12.5 grams

Finding the time taken:

Number of half-lives:

We know that in the relation:

, n is the number of half-lives taken

replacing the given values:

12.5 / 100 = 1/2ⁿ

1/8 = 1/2ⁿ

2ⁿ = 8

2ⁿ = 2³

n = 3

Hence, it took 3 half-lives to reduce the mass to 12.5 grams

Number of years:

Time taken = 3 half-lives

we know that one half-life is 5715 years, replacing that value:

Time taken = 3*(5715) years

Time taken = 17145 years

Therefore, after 17145 years, a 100 gram sample of carbon will decay and only 12.5 grams will remain