Answer :
It will take 267 milliseconds for a sample of radon-218 to decay from 99 grams to 0. 50 grams.
We know that half life of a first order reaction is given by: [tex]t_{1/2} = 0.693/k[/tex]
where k = rate of reaction
Given half life = 35 milliseconds
So from this we get k = 0.0198
Now we know that rate of first order reaction is given by: [tex]kt= 2.303 * log(R'/R)[/tex]
where t= time
R'= initial amount = 99 g
R= final amount= 0.50 g
k= rate of reaction = 0.0198
Putting values of these in above equation we get t=267 milliseconds.
i.e. It will take 267 milliseconds for a sample of radon-218 to decay from 99 grams to 0. 50 grams.
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