The amount of a uniformly distributed radioactive contaminant contained in a closed reacto...

The amount of a uniformly distributed radioactive contaminant contained in a closed reactor is measured by its concentration c (becquerel/liter or Bq/L). The contaminant decreases at a decay rate proportional to its concentration; that is

Decay rate = −kc

where k is a constant with units of day⁻¹. Therefore, according to Eq. (1.14), a mass balance for the reactor can be written as

(a) Use Euler’s method to solve this equation from t = 0 to 1 d with k = 0.175 d⁻¹. Employ a step size of Δt = 0.1 d. The concentration at t = 0 is 100 Bq/L.

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(b) Plot the solution on a semilog graph (i.e., ln c versus t) and determine the slope. Interpret your results.

Equation 1.14: