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Radon-222 is a radioactive gas with a half-life of 3.82 days. How long would it take for fifteen-sixteenths of a sample of radon-222 to decay?

15.28 days

30.56 days

45.84 days

49.66 days

Verified Answer :

Use the formula in terms of half life from the normal exponential functions 

N(t) = N(0) (1/2) ^ (t/thalf) 

N(0) is the original quantity 

N(t) = quantity remaining at time t 

t is the time 


thalf is half life 

1/16 = (1/2)^(t/3.82) 

16 = 2^(t/3.82) 

4 = t/3.82 

t = 15.28 days

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