Question

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

Answer 1

42960 years

Step-by-step 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