A certain monovalent metal has density $10\mathrm{.}72$ g$/$cm$^3$ and molar mass $118$ g$/$mol$.$ Calculate $($a$)$ the number density of conduction electrons, $($b$)$ the Fermi energy, $($c$)$ the Fermi speed, and $($d$)$ the de Broglie wavelength corresponding to this electron speed.