How to calculate the maximum kinetic energy of photo emitted electrons if uv radiation has a wavelength of 275 nm?

You calculate the energy of a quantum of the UV light and subtract the work function of the metal.

This is a problem involving the photoelectric effect.

The equation for the photoelectric effect is

##E_K = hf –ø##, where

##E_K## is the maximum kinetic energy of the photoelectron ##h## is Planck's constant ##f## is the frequency of the light ##ø## is the work function of the metal

Let's assume that the metal is magnesium. Then

##ø = "3.88 eV" × (1.602 × 10^-19 "J")/"1 eV" = 6.216 × 10^-19 "J"##

##hf = (hc)/λ = (6.62606896 × 10^-34 "J·s" × 2.998 × 10^8 "m·s"^-1)/(275 × 10^-9 "m") = 7.224 × 10^-19 "J"##

Then

##E_K = hf - ø = 7.224 × 10^-19 "J" – 6.216 × 10^-19 "J" = 1.01 × 10^-19 "J"##