OpenStax College Physics, Chapter 29, Problem 12 (Problems & Exercises)

This is College Physics Answers with Shaun Dychko. An electron is being ejected from calcium metal with a kinetic energy of 2.00 electron volts and we are told that the binding energy of the electron was 2.71 electron volts and the question is what wavelength of photon did this? So the kinetic energy of the ejected electron is the energy of the photon and we assume that all of that photon's energy is absorbed by the electron and then minus the binding energy. We can replace frequency with an expression in terms of wavelength and we know that from the wave equation that the speed of light is wavelength multiplied by frequency and we can divide both sides by λ to solve for f so f is c over λ and we replace frequency with this expression c over λ and then we add binding energy to both sides and then switch the sides around and we have hc over λ is the kinetic energy plus the binding energy. Then we want to solve for λ so we are going to multiply both sides by λ over kinetic energy plus binding energy then we get an expression for wavelength: it's Planck's constant times speed of light divided by the kinetic energy of the electron plus the binding energy. I can use this convenient version of Planck's constant when it's being multiplied by speed of light, I am going to write 1240 electron volt nanometers and that'll give us an answer in nanometers since the electron volts here will cancel with the electron volts that we have on the bottom. So we have two electron volts of kinetic energy plus 2.71 electron volts of binding energy and this all works out to 263 nanometers and this is ultraviolet light.