The radioisotope radon-222 has a half-life of 3.8 days. how much of a 73.9-gram sample of radon-222 would be left after approximately 23 days?

There will be 1.11 grams of the sample of radon-222 left. This answer can be obtained using the formula of half life to get the rate constant which will be used in another equation later on.

Half-life (t) = ln2/k = 3.8 days

k = 0.182407/day

Using the general equation of a first order reaction:

Ca/Cao = 1/e^(kt)
Ca/Cao = 0.01506 --> fraction of radon-222 left

This means that 1.51% of the original amount remains, so 1.51% of 73.9 is 1.11 grams.