Question

In this problem we use observations of the radioactive gas 85Kr to determine the characteristic time for exchange of air between the northern and southern hemispheres. We consider a 2-box model where each hemisphere is represented by a well-mixed box, with a rate constant k (yr-1 ) for mass exchange between the two hemispheres. Our goal is to derive the residence time τ = 1/k of air in each hemisphere. Krypton-85 is emitted to the atmosphere during the reprocessing of nuclear fuel. It is removed from the atmosphere solely by radioactive decay with a rate constant kc = 6.45x10-2 yr-1 . The sources of 85Kr are solely in the northern hemisphere and their magnitudes are well known due to regulation of the nuclear industry. Atmospheric concentrations of 85Kr are fairly well known from ship observations. In 1983 the global 85Kr emission rate was E = 15 kg yr-1 , the total atmospheric mass of 85Kr in the northern hemisphere was MN = 93 kg, and the total atmospheric mass of 85Kr in the southern hemisphere was MS = 86 kg.

The global emission rate of 85Kr was increasing during the 1980s at the rate of 3% yr-1 . Justify the assumption d(MN - MS)/dt = 0. [Hint: use the mass balance equation for (MN - MS) to determine the time scale needed for (MN - MS) to adjust to steady state following a perturbation.]

Please don't copy and paste from another post with this question, all of those answers are wrong.

Answer 1