If a sample contains 50g of carbon 14 and 50g of nitrogen 14 , how many lives has it undergone ?
half of the C14 has decayed to N14 , so, one half-life
To determine the number of half-lives that the sample has undergone, we need to compare the ratio of carbon-14 to nitrogen-14 in the sample. The half-life of carbon-14 is approximately 5730 years.
1. Calculate the number of moles of carbon-14:
- The molar mass of carbon-14 is approximately 14 g/mol.
- Number of moles of carbon-14 = mass of carbon-14 / molar mass of carbon-14.
= 50 g / 14 g/mol
≈ 3.571 moles
2. Calculate the number of moles of nitrogen-14:
- The molar mass of nitrogen-14 is also approximately 14 g/mol.
- Number of moles of nitrogen-14 = mass of nitrogen-14 / molar mass of nitrogen-14.
= 50 g / 14 g/mol
≈ 3.571 moles
3. Compare the ratio of carbon-14 to nitrogen-14:
- The ratio of carbon-14 to nitrogen-14 is 1:1 (since both have the same mass in this case).
4. Calculate the number of half-lives:
- Since the ratio is 1:1, it means that all carbon-14 has been converted into nitrogen-14.
- In one half-life, half of the initial amount of carbon-14 decays.
- Since all the carbon-14 has decayed, it means the number of half-lives is equal to the natural logarithm of 2 (ln(2)) divided by the decay constant of carbon-14.
≈ ln(2) / (5730 years)
So, the sample has undergone approximately ln(2) / (5730 years) half-lives.
To determine the number of lives a sample has undergone, we need to use the concept of half-life. The half-life is defined as the time it takes for half of a substance to decay.
In this case, we have two isotopes: carbon-14 and nitrogen-14. Carbon-14 undergoes radioactive decay and is converted into nitrogen-14. The half-life of carbon-14 is approximately 5730 years.
To find out how many half-lives have occurred, we can compare the amount of carbon-14 to nitrogen-14 in the sample.
Initially, we have 50g of carbon-14 and 50g of nitrogen-14. This means that half of the 50g of carbon-14 (25g) has already decayed to form nitrogen-14.
Let's calculate the number of half-lives that have occurred:
- 25g of carbon-14 has decayed to form 25g of nitrogen-14. This represents one half-life.
- After another half-life, half of the remaining 25g of carbon-14 (12.5g) would decay, leaving 12.5g of carbon-14 and 37.5g of nitrogen-14.
- After two half-lives, half of the remaining 12.5g of carbon-14 (6.25g) would decay, leaving 6.25g of carbon-14 and 43.75g of nitrogen-14.
Therefore, the sample has undergone two half-lives.
Remember, each half-life takes approximately 5730 years for carbon-14. Multiplying the number of half-lives by the half-life duration will give us an estimate of the elapsed time. In this case, the elapsed time would be around 2 x 5730 = 11460 years.