Lithium has a work function of $2\mathrm{.}30$ eV$.$ Mercury has a work function of $4\mathrm{.}50$ eV$.($i$)(10$ points$)$ What are the cutoff wavelengths for each metal, in meters? $[$Hint: you can save time by noting that hc $=1240$ eV$$nm$.]($ii$)(5$ points$)$ If light with a wavelength of $400$ nm is used, which of the metals will exhibit the photoelectric effect? Show your work, or no credit will be given. $($iii$)(5$ points$)$ For the metal or metals here that exhibit the photoelectric effect, what is the maximum kinetic energy, in eV$,$ of the emitted electrons when the $400$ nm light is used?