Assume you have $10000$ pure carbon $($graphite$)$ particles of a$)5$ nm diameter, b$)500$ nm diameter, and c$)50000$ nm diameter. These particles are collected in a long cylindrical tube of sufficiently large diameter held vertically. Determine the distribution of each of these particles along the vertical length of the tube. Show this distribution with a plot. How far up are you likely to find at least $1$ particle for each of these particle sizes. Explain why not all the particles are settled at the bottom of the cylinder. Will the distribution of these particles change based on what time of the day it is or what month of the year it is$?$