A nuclear power station is situated in Coal Valley, which is a roughly rectangular valley that is 5 km long, 2 km wide, and 200 m deep. You have been asked to evaluate the effects of a worst- case scenario where the reactor housing fails, and radiation is released to the atmosphere. In your evaluation, you determine that 120 kg of lodine-131 (a radioisotope that causes thyroid gland and liver damage) could be released into the atmosphere. a. Assuming the release of lodine-131 was very rapid and all of it was uniformly distributed through the valley's atmosphere with none escaping the valley, what would the concentration of lodine-131 be in the valley's air? Your answer should be expressed in units of ppmv, and you may assume an atmopheric pressure of 1.0 atm and a temperature of 20°C.
b. Assuming the lodine-131 concentration you calculated in part (a) is the initial concentration in the valley, you now want to determine the time it will take for the concentration to decrease to the safe limit of 1.0% 10-5 ppmv. The average windspeed through the valley (entering at one end and exiting at the other) is only 1.5 m/min. However, lodine-131 also is removed by two other processes: 1) radioactive decay with a half life of 8.1 days, and 2) sedimentation to the ground with a rate constant of 0.02 d^-1. Draw a picture of the situation, and label the appropriate.
c. Now derive an equation that expresses the concentration of lodine-131 in the valley's air as a function of the time since the accident. Use the equation to determine the time needed for the concentration to decrease to a safe level.