If a sample contains 25 g or carbon-14 and 75 g of nitrogen-14, how many half-lives has it undergone
To determine the number of half-lives undergone by the sample, we need to compare the amount of carbon-14 (C-14) with the amount of nitrogen-14 (N-14) and calculate the ratio.
Carbon-14 undergoes radioactive decay, transforming into nitrogen-14 over time. The half-life of carbon-14 is approximately 5730 years, meaning that after 5730 years, half of the original amount of carbon-14 in a sample will have decayed.
Let's calculate the ratio of C-14 to N-14 in the given sample:
- The sample contains 25 g of C-14 and 75 g of N-14.
- The total mass of the sample is 25 g + 75 g = 100 g.
- We can express the ratio of C-14 to N-14 as 25 g / 75 g = 1/3.
By comparing the ratio of C-14 to N-14 with the known ratio after each half-life, we can determine the number of half-lives undergone.
- After one half-life, half of the original C-14 would have decayed, leaving 1/2 of the original amount. The ratio would be 1/2.
- After two half-lives, 1/4 of the original C-14 would remain. The ratio would be 1/4.
- After three half-lives, 1/8 of the original C-14 would remain. The ratio would be 1/8.
In our sample, the ratio is 1/3, which does not match any of the calculated ratios. Therefore, the number of half-lives undergone is less than one, indicating that the sample hasn't undergone any complete half-lives.
In summary, the sample has not undergone any complete half-lives of carbon-14 decay.
To determine the number of half-lives the sample has undergone, we need to know the half-life of carbon-14. The half-life of carbon-14 is approximately 5730 years.
To calculate the number of half-lives, we divide the amount of carbon-14 remaining by the initial amount of carbon-14.
Initial amount of carbon-14 = 25 g
Remaining amount of carbon-14 = 25 g
Number of half-lives = log(base 2) (remaining amount / initial amount)
Number of half-lives = log(base 2) (25 g / 25 g)
Number of half-lives = log(base 2) (1)
Since log(base 2) (1) = 0, the sample has undergone 0 half-lives.
Therefore, the sample has not undergone any half-lives.