a$)$ Calculate the mass of a monolayer of hydrated sodium ions $($in g$.)($atomic weight of sodium $=23\frac{g}{m}$ole, atomic weight of water $=18\frac{g}{m}$ole, atomic diameter of the hydrated ion $=0\mathrm{.}36nm,1$mole$=6\mathrm{.}02{10}^{23}$ atoms$)$ on one square meter of smooth surface. There are $4$ water molecules closely associated with each sodium ion. The hydrated sodium ion can be assumed to be a sphere. Assume packing pattern $"A"$ below. $(10$ points$)$

b$)$ If this sodium were adsorbed to one surface of a smooth gold foil $1c{m}^2$ in area and $0\mathrm{.}1mm$ thick, what would be the ratio $($by mass$)$ of hydrated sodium ion to gold $($density of gold $=19\mathrm{.}3\frac{g}{c}{m}^3)?(10$ points$)$