If a sample contains 50g of carbon 14 and 50g of nitrogen 14 , how many lives has it undergone ?
the inital mass was 100g, it is now at 50 g, so it is at the first half life.
To determine the number of lives the sample has undergone, we need to understand the concept of half-life and the decay of Carbon-14.
Carbon-14 (C-14) is a radioactive isotope that undergoes radioactive decay, turning into Nitrogen-14 (N-14) over time. The half-life of Carbon-14 is approximately 5730 years.
The half-life refers to the time it takes for half of the radioactive atoms in a sample to decay. After one half-life, half of the Carbon-14 in the sample would have decayed into Nitrogen-14, and so on.
Now, let's calculate the number of half-lives the sample has undergone:
1. Start with the original amount of Carbon-14: 50g
2. After one half-life, half of the Carbon-14 would decay to Nitrogen-14.
Remaining Carbon-14: 50g / 2 = 25g
Nitrogen-14 produced: 50g - 25g = 25g
3. After the second half-life:
Remaining Carbon-14: 25g / 2 = 12.5g
Nitrogen-14 produced: 25g - 12.5g = 12.5g
4. After the third half-life:
Remaining Carbon-14: 12.5g / 2 = 6.25g
Nitrogen-14 produced: 12.5g - 6.25g = 6.25g
We can continue this process until the remaining amount of Carbon-14 is negligible.
Therefore, based on the calculations, the sample has undergone three half-lives.