Assumptions:

$1.$ Dust particles were suspended evenly in the earth$$s troposphere, which has an average height of $5$ km;

$2.$ All of the particles have the same size of $1$ micrometer, the particles are spherical with a density of $1$ g$/$cm$3$;

$3.$ Assume that the falling of the dust particles is in laminar regime, meaning that the drag force has an equation of F $=3,$ and the falling of the particles reach steady state instantaneously. In this equation, is the dynamic viscosity of air, is the particle diameter, and is the relative velocity between the particle and the air.

Question:

Check the unit of drag force, is the unit in N $($Newton$)?$

Assume that there is no mixing in the earth$$s troposphere. How many years does it take so that $95\%$ of the particles settle onto the ground?

Assuming that the earth's atmosphere is well mixed, how many years does it take so that $95\%$ of the particles settle onto the ground? Please show all steps. Thank you.