3. Assume a collection of spherical dust gains of radius r in a cloud of dust and hydrogen of temperature T, dust number density 71d and hydrogen number density uH. Assmne that all the hydrogen atoms are moving at velocity or which is appropriate for the temperature T. {a} What is the number of hydrogen atoms hitting any given dust grain per second, call it N '1'" {b} What is the number of hydrogen atoms striking any dust gain at all (per mug}? {c} Assume that every hydrogen atom 1which strikes a dust gain sticks to it long enough to nd another hydrogen atom., and to combine with it to form a hydrogen molecule H2, which is then released back into the gas phase immediately. What is the timescale for forming the H2 molecules1 based on your results from Farts {a} and (h); {d} Calculate the numerical value of t from the your result in Part ((3)1 if 'r' = [1.1 pm, T = ll] K, the initial value of Hg = 3m} (21113, and f: = ill12. {e} What does the your result from Part {d} imply for the minimum age of molecular hydrogen clouds