Answer:
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;
- 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