$1.$ A parallel light beam at a wavelength of $200$ nm is incident normally on the surface of a metal of which the work function is $3\mathrm{.}44$ eVa$)$ Determine the shortest de Broglie wavelength of the electrons photoelectrically ejected from the surface.b$)$ If the intensity of the light beam is $0\mathrm{.}95$ W$/$m$?,$ determine the number of electrons ejected from a square centimeter of the metal surface each second. Assume that the probability of each photon being absorbed by a electron is $0\mathrm{.}3.$c$)$ Determine the potential that can stop the electrons from being ejected from the metal surlace.