The work function for platinum is $6\mathrm{.}35$ eV$.$ Ultraviolet light of wavelength $133$ nm is incident on the clean surface of a platinum sample. We wish to predict the stopping voltage we will need for electrons ejected from the surface.

$($a$)$ What is the photon energy of the ultraviolet light?

$($b$)$ How do you know that these photons will eject electrons from platinum?

$($c$)$ What is the maximum kinetic energy of the ejected photoelectrons?

$($d$)$ What stopping voltage would be required to arrest the current of photoelectrons?