Answer :
Answer:
Mass of original sample = 100 g
Explanation:
Half life of cesium-137 = 30.17 years
[tex]t_{1/2}=\frac {ln\ 2}{k}[/tex]
Where, k is rate constant
So,
[tex]k=\frac{\ln2}{t_{1/2}}[/tex]
[tex]k=\frac{\ln2}{30.17}\ year^{-1}[/tex]
The rate constant, k = 0.02297 year⁻¹
Time = 90.6 years
Using integrated rate law for first order kinetics as:
[tex][A_t]=[A_0]e^{-kt}[/tex]
Where,
[tex][A_t][/tex] is the concentration at time t
[tex][A_0][/tex] is the initial concentration
Initial concentration [tex][A_0][/tex] = ?
Final concentration [tex][A_t][/tex] = 12.5 grams
Applying in the above equation, we get that:-
[tex]12.5\ g=[A_0]e^{-0.02297\times 90.6}[/tex]
[tex][A_0]=\frac{12.5}{e^{-0.02297\times 90.6}}\ g=100\ g[/tex]
Mass of original sample = 100 g