If a 20 gram sample of a radioactive substance has a half-life of 6000 years, how many grams would be present after 18000 years?

Radioactive decay law

N =N₀exp(-λt)=
=N₀exp(-ln2•t/T)=
=20exp(-0.693•18000/6000) = 2.5 g

To determine the amount of grams of the radioactive substance that would be present after 18000 years, we need to use the concept of half-life.

The half-life of a radioactive substance is the amount of time it takes for half of the substance to decay. In this case, the half-life is 6000 years.

With each half-life, half of the substance decays, and the other half remains. So after 6000 years, half of the substance remains, which is 10 grams since we started with a 20 gram sample.

Now, we can find the number of half-lives that occur in 18000 years by dividing the total time by the half-life:

18000 years / 6000 years = 3 half-lives.

Since each half-life reduces the amount by half, we need to multiply the original sample (20 grams) by (1/2) three times:

(20 grams) * (1/2) * (1/2) * (1/2) = 2.5 grams.

Therefore, after 18000 years, there would be 2.5 grams of the radioactive substance present.