Question

you are given a bone sample and, when you measure the amount of carbon and nitrogen in the sample, you find that the sample contains 625 mg of C-14 (parent atom) and 1875 mg of N-14 (daughter atom). If Carbon-14 has a half-life of 5730 years, how old is the sample?

Answer 1

The bone sample is approximately 5730 years old, based on the given amounts of carbon-14 and nitrogen-14 in the sample. Since each half-life represents 5730 years, the age of the bone sample is approximately 5730 years. *Mass of C-14 or N-14 atoms = mass of one mole of atoms / Avogadro's number.

Step-by-step explanation:

To calculate the age of the bone sample, we need to determine the number of half-lives that have occurred since the bone died and the carbon-14 began to decay. First, let's find the initial number of carbon-14 atoms in the sample:

Initial number of carbon-14 atoms = 625 mg / (14 g/mol)*(6.022×10^23 atoms/mol) = (625×10^-3 g) / (14 g/mol)*(6.022×10^23 atoms/mol) = (625×10^-3 / 14)×(6.022×10^23) atoms = appoximately 2.7×10^22 atoms Now, we need to compare this to the current number of carbon-14 atoms in the sample, which is given by 1875 mg / (14 g/mol)*(6.022×10^23 atoms/mol).

Let's find the number of half-lives that have occurred: Number of half-lives = log2(current number of carbon-14 atoms / initial number of carbon-14 atoms) = log2((1875×10^-3 g) / (14 g/mol)*(6.022×10^23 atoms/mol) / (2.7×10^22 atoms) ≈ log2(0.5) = 1 Since each half-life represents 5730 years, the age of the bone sample is approximately 5730 years. *Mass of C-14 or N-14 atoms = mass of one mole of atoms / Avogadro's number.