Question

You receive a sample in your lab. You are tasked to date the sample using radiocarbon dating. The sample is expected to have 0.005 g of Carbon-14. It currently has 0.002 g of Carbon-14. How old is the sample? (Hint; The half-life of Carbon-14 is 5,730 years).

Answer 1

Using the half-life of Carbon-14, which is 5,730 years, the sample with an initial 0.005 g of C-14 that now contains 0.002 g of C-14 is determined to be approximately 9,168 years old.

Step-by-step explanation:

To determine how old the sample is using radiocarbon dating, we will use the concept of half-lives of Carbon-14. The half-life of Carbon-14 (C-14) is 5,730 years, which means that every 5,730 years, the amount of C-14 in a sample is reduced by half due to radioactive decay.

In your sample, the original amount of C-14 was 0.005 g, and it currently has 0.002 g. To find out how many half-lives have passed, we need to calculate how many times 0.005 g needs to be halved to reach 0.002 g:

• After one half-life (5,730 years), 0.005 g becomes 0.0025 g
• After two half-lives (11,460 years), 0.0025 g becomes 0.00125 g

Since the current amount is 0.002 g, which is more than 0.00125 g, we know that the sample is between one and two half-lives old. We can now use a proportion to find the exact age:
(0.005 g - 0.002 g) / (0.005 g - 0.0025 g) = (Age - 5730 years) / (11460 years - 5730 years)

Solving for Age gives you:

Age = 5730 years + (0.003 g / 0.0025 g) * (11460 years - 5730 years)

Age ≈ 5730 years + 0.6 * 5730 years = 5730 years + 3438 years ≈ 9168 years

Therefore, the sample is approximately 9,168 years old.