$($Problem #$6)$

$($a$)$ When electromagnetic radiation with wavelength $=2000$ is incident on a clean tungsten

plate in a vacuum, the maximum kinetic energy observed amongst the electrons ejected is $1\mathrm{.}64$

$eV.$ Calculate the threshold wavelength above which it will not be possible to eject electrons

from tungsten metal. Show your work and express your answer in $nm.$

$($b$)$ The maximum kinetic energy observed amongst electrons ejected from potassium metal by

electromagnetic radiation with frequency $v=1\mathrm{.}63{10}^{15}{s}^{-1}$ is $7\mathrm{.}2{10}^{-19}J.$ Calculate the

wavelength associated with the motion of an ejected electron that has this maximum kinetic

energy. Show your method clearly and express your answer in $nm.$