Answer: a) 3.85 days
b) 10.54 days
Explanation:-
Expression for rate law for first order kinetics is given by:

where,
k = rate constant = ?
t = time taken for decomposition = 3 days
a = let initial amount of the reactant = 100 g
a - x = amount left after decay process = 
First we have to calculate the rate constant, we use the formula :
Now put all the given values in above equation, we get


a) Half-life of radon-222:


Thus half-life of radon-222 is 3.85 days.
b) Time taken for the sample to decay to 15% of its original amount:
where,
k = rate constant = 
t = time taken for decomposition = ?
a = let initial amount of the reactant = 100 g
a - x = amount left after decay process = 


Thus it will take 10.54 days for the sample to decay to 15% of its original amount.
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Answer:
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The answer to this question is True