Respuesta :
Answer:
a) The half life of the radioactive sample is 0.22 years.
b) It will take 0.16 years to sample to decay to 40% of its original amount.
Explanation:
a) Initial amount of radioactive substance = [tex][A_o][/tex]
Final amount of radioactive substance after 1 year= [tex][A]=(100\%-96\%)[A_o]=4\%[A_o]=0.04[A_o][/tex]
Decay constant = k
Decaying of radio active sample follows first order kinetics:
[tex][A]=[A_o]\times e^{-kt}[/tex]
[tex]0.04[A_o]=[A_o]\times e^{-k\times 1 year}[/tex]
[tex]k=3.2189 year^{-1}[/tex]
Half life of the sample = [tex]t_{1/2}[/tex]
[tex]t_{1/2}=\frac{0.693}{k}[/tex]
[tex]=\frac{0.693}{3.2189 year^{-1}}=0.2152 year\approx 0.22 year[/tex]
The half life of the radioactive sample is 0.22 years.
b)
Initial amount of radioactive substance = [tex][A_o][/tex]
Final amount of radioactive substance after t years= [tex][A]=(100\%-40\%)[A_o]=60\%[A_o]=0.6[A_o][/tex]
Decay constant = k = [tex]3.2189 year^{-1}[/tex]
Decaying of radio active sample follows first order kinetics:
[tex][A]=[A_o]\times e^{-kt}[/tex]
[tex]0.6[A_o]=[A_o]\times e^{-3.2189 year^{-1}\times t}[/tex]
Solving for t:
t = 0.1587 years ≈ 0.16 years
It will take 0.16 years to sample to decay to 40% of its original amount.
