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19. Radioactive copper, Cu, is found in quantities exceeding pollution standards in the sediments of a
reservoir in a routine check on Monday. The standard allows up to 14 ppm/cubic meter of sediment.
On Monday, 59ppm/cubic meter were measured. The half life of Cu is 12.7 hours. When will the
pollution level return to 14ppm?
29

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dsdrajlin

It will take 26 h for the concentration of radioactive Cu to decrease from 59 ppm/m³ to 14 ppm/m³.

What is radioactive decay?

Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation. It follows first-order kinetics.

  • Step 1. Calculate the rate constant.

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

  • Step 2. Calculate the required time for the concentration to decrease.

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.

Learn more about radioactivity here: https://brainly.com/question/2320811

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