Answer :
The time needed to decrease reactant concentration based on its half-life is 68.47 seconds.
We need to know about the half-life of the radioactive elements to solve this problem. The radioactive element will decay over time and follow the equation
N = No(1/2)^(t/t'')
where N is the final quantity, No is the initial quantity, λ is the decaying constant, t is time and t'' is the half-life of a radioactive element.
From the question above, we know that
t'' = 41.3 s
No = 6.5 m
N = 2.06 m
By substituting the given parameters, we can calculate the time taken
N = No(1/2)^(t / t'')
2.06 = 6.5 . (1/2)^(t / 41.3)
0.32 = (1/2)^(t / 41.3)
⁰'⁵log(0.32) = t / 41.3
1.66 = t / 41.3
t = 68.47 seconds
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