Problem: 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?a. 58.28b. 0.1824c. 19.908d. 0.1597e. 10.49

FREE Expert Solution

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:


ln [N]t=-kt+ln [N]0


where:

[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:


t12=ln 2k


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Problem Details

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?

a. 58.28
b. 0.1824
c. 19.908
d. 0.1597
e. 10.49

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