The isotope carbon-14, 146C, is radioactive and has a half-life of 5730 years. If you start with a sample of 1000 carbon-14 nuclei, how many will still be around in 22920 years?
I got 62.5 atoms, am I correct??
Thank you!!
it is 4 half-lives, so 1/16 is left. You are correct.
To determine the number of carbon-14 nuclei remaining after 22920 years, you can use the formula:
N(t) = N₀ * (1/2)^(t / tₕₑ)
where:
N(t) is the number of carbon-14 nuclei remaining after time t,
N₀ is the initial number of carbon-14 nuclei,
t is the time elapsed, and
tₕₑ is the half-life of carbon-14.
In this case, N₀ = 1000, t = 22920 years, and tₕₑ = 5730 years.
Plugging these values into the formula, we get:
N(22920) = 1000 * (1/2)^(22920/5730)
Now, let's calculate:
N(22920) = 1000 * (1/2)^(4)
N(22920) = 1000 * 1/16
N(22920) = 62.5
So, according to the calculation, you are correct. There will be approximately 62.5 carbon-14 nuclei remaining after 22920 years.