What size does a particle have to be if it is to have a roughly 50% chance of passing to the atmosphere of the southern hemisphere after being

What size does a particle have to be if it is to have a roughly 50% chance of passing to the atmosphere of the southern hemisphere after being emitted to the mid-troposphere in the mid-latitudes of the northern hemisphere? Use Stokes law and assume that the particle is spherical, with a density of 2 g/cm3, and its only exit pathways from the atmosphere of the northern hemisphere are dry fallout and convection to the atmosphere of the southern hemisphere.