3. Nuclear Disasters. The Zaporizhzhia Nuclear Power Plant in Ukraine is responsible for ~20% of Ukraines energy source, but is under threat from the ongoing war. In the event of an explosion, much of the nuclear material (cesium, nickel, etc.) will be transported by particles that are in the size range of 300 nm to 15 m. How long particles last in the atmosphere and can be transported is determined by the particles deposition velocity. The lifetime of the particle (how long to get down to 1/e of the initial concentration) can be roughly calculated by dividing the deposition velocity by atmospheric boundary layer height. This is a first order loss process. Show your work for full credit.

a. Assuming a boundary layer height of 1 km, how long in days will a 10m particle last in the atmosphere? Use the figure below to estimate deposition velocity for 10 m particles.

b. The annual average wind speed for the capital of Ukraine is 26 km/hr (~16 mph). Lets make a bold assumption that the wind speed is constant, and that it is blowing in a straight line from Zaporizhzhia to Stockholm. How long will it take to travel from Zaporizhizhia to Stockholm?

c. What fraction of the 10 m particulate mass initially emitted from the explosion will still be present in the atmosphere by the time the airmass gets to Stockholm? (Hint: you can convert the deposition velocity into a rate loss constant by dividing by the boundary layer height you should have a rate constant in units of s-1).

d. Now compare this time to the half-lives of I131 and Cs137. Considering loss to both deposition and radioactive decay, what percentage of the initial I131 and Cs137 emitted from the explosion will be remaining in the atmosphere in Stockholm?

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