Answer:
It will take 6.6 hours for 75% of the lead to decay.
Explanation:
The radioactive decay follows first order rate law
The half life and rate constant are related as
[tex]k=rate constant=\frac{0.693}{halflife}=\frac{0.693}{3.3}=0.21h^{-1}[/tex]
The rate law for first order reaction is
[tex]time=\frac{1}{k}(ln[\frac{A_{0}}{A_{t}}][/tex]
Where
A0 = initial concentration = 1 g
At= final concentration = 0.25 g (as 75% undergoes decay so 25% left]
[tex]time=\frac{1}{0.21}(ln(\frac{1}{0.25})=6.6hours[/tex]
