It will take 26 h for the concentration of radioactive Cu to decrease from 59 ppm/m³ to 14 ppm/m³.
Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation. It follows first-order kinetics.
Radioactive copper has a half-life (th) of 12.7 h. We can calculate the rate constant (k) using the following expression.
k = ln2 / th = ln2 / 12.7 h = 0.0546 h⁻¹
On Monday, the concentration of Cu was 59 ppm/m³ ([Cu]₀).
We want to know the required time (t) for it to decrease to 14 ppm/m³ ([Cu]).
We will use the following expression.
ln ([Cu]/[Cu]₀) = -k × t
ln [(14 ppm/m³)/(59 ppm/m³)] = -0.0546 h⁻¹ × t
t = 26 h
It will take 26 h for the concentration of radioactive Cu to decrease from 59 ppm/m³ to 14 ppm/m³.
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