A small comet nucleus consists of a spherical ice chunk of radius R=50m at temperature T=200K. As it approaches the Sun, solar heating causes the ice to sublime directly into water vapor at the surface. The sublimed vapor forms a thin atmospheric shell around the nucleus before escaping to space.
The sublimation rate follows the empirical relation m˙=αA2πkBTM where m˙ is the mass loss rate, A is the surface area, M=18g/mol is the molar mass of water, and α=2.4×10−4Pa is the vapor pressure at this temperature.
Find the number density n (molecules per unit volume) of water vapor in the thin atmospheric shell, assuming the vapor moves radially outward with the most probable speed from kinetic theory before escaping to space.
Use: kB=1.38×10−23J/K, Avogadro's number NA=6.02×1023mol−1