We’re being asked to calculate the time it takes (in years) for the sample to be reduced to 1.00 mg of Rn-222 if there are 36.0 g of Rn-222 initially.
Recall that radioactive/nuclear decay of isotopes follows first-order kinetics, and the integrated rate law for first-order reactions is:
[N]t = concentration at time t
k = decay constant
t = time
[N]0 = initial concentration.
Also, recall that half-life is the time needed for the amount of a reactant to decrease by 50% or one-half.
The half-life of a first-order reaction is given by:
The half-life of 222Rn is 3.80 days. If a sample contains 36.0 g of Rn-222, how many years will it take for the sample to be reduced to 1.00 mg of Rn-222?
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