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Every mrtal has a definite work function...

Every mrtal has a definite work function. Why do all photoelectrons not come out with same energy, if incident radiation is monochromatic? Why is there an energy distribution of photoelectrons?

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In a photoelectric effect set up, a point source of light of power 3.2 xx10^(-3) W emits monoenergetic photons of energy 5eV.The source is located at a distance of a stationary metallic sphere of work function 3eV and radius 8xx10^(-3)m .The efficiency of photoelectron emission is one for every 10^(6) incident photons.Assume that the sphere is isolated and initially neutral and the photoelectrons are initially swept away after emission. Calculate the number of photoelectrons emitted per second.

In a photoelectric effect set up, a point source of light of power 3.2 xx10^(-3) W emits monoenergetic photons of energy 5eV.The source is located at a distance of a stationary metallic sphere of work function 3eV and radius 8xx10^(-3)m .The efficiency of photoelectron emission is one for every 10^(6) incident photons.Assume that the sphere is isolated and initially neutral and the photoelectrons are initially swept away after emission. Find the ratio of the wavelength of incident light to the de Broglie wavelength of the fastest phtotelectrons emitted.