The isotope carbon-14, 614 𝐶𝐶, is radioactive and has a half-life of 5 730 years. If you start with a sample of 1 000 carbon-14nuclei, how many nuclei will still be undecayed in 25 000 years?
Question
The isotope carbon-14, 614 𝐶𝐶, is radioactive and has a half-life of 5 730 years. If you start with a sample of 1 000 carbon-14nuclei, how many nuclei will still be undecayed in 25 000 years?
Solution
To solve this problem, we need to use the formula for radioactive decay, which is:
N = N0 * (1/2)^(t/T)
where:
- N is the final quantity of the substance
- N0 is the initial quantity of the substance
- t is the time that has passed
- T is the half-life of the substance
In this case, we know that:
- N0 = 1 000 nuclei
- t = 25 000 years
- T = 5 730 years
So, we can substitute these values into the formula to find N:
N = 1 000 * (1/2)^(25 000 / 5 730)
First, calculate the exponent:
25 000 / 5 730 = 4.36 (approximately)
Then, calculate the power of 1/2:
(1/2)^4.36 = 0.052 (approximately)
Finally, multiply this by the initial quantity:
N = 1 000 * 0.052 = 52 (approximately)
So, after 25 000 years, approximately 52 of the original 1 000 carbon-14 nuclei will still be undecayed.
Similar Questions
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