How old is a bone if it now. 3125 of C-14 when it originally had 80.0g of C-14

42960 years

Explanation:

We are given;

Remaining mass of C-14 in a bone is 0.3125 g Original mass of C-14 on the bone is 80.0 g Half life of C-14 is 5370 years

We are required to determine the age of the bone;

Using the formula; Remaining mass = Original mass * 0.5^n, where n is the number of half lives.

Therefore;

0.3125 g = 80.0 g * 0.5^n

3.90625 * 10^-3 = 0.5^n

Introducing logarithm on both sides;

log 3.90625 * 10^-3 = n log 0.5

Solving for n

n = log 3.90625 * 10^-3 : log 0.5

= 8

Therefore, the number of half lives is 8 But, 1 half life is 5370 years Therefore;

Age of the rock = 5370 years * 8

= 42960 years

Thus, the bone is 42960 years old