OpenStax College Physics, Chapter 29, Problem 4 (Problems & Exercises)

This is College Physics Answers with Shaun Dychko. The binding energy of silver is 4.73 electron volts and the question is asking what is the longest wavelength electromagnetic radiation that can eject an electron from silver? Here's a formula for the kinetic energy of the ejected electron and it's Planck's constant times the frequency of the photon minus the binding energy and we are going to set this equal to zero here because we want to find what is the lowest possible frequency in which case you have the electron ejected with the lowest possible kinetic energy, which is zero. We'll add binding energy to both sides here and we've Planck's constant times frequency then equals the binding energy, divide both sides by h and you get frequency is binding energy over Planck's constant. Now we want to know the wavelength though so we will use this wave equation, which says speed of light equals the wavelength times the frequency and we will divide both sides by f and we have λ then is c over f. Now we are dividing by f and we are going to instead multiply by the reciprocal of this fraction I am going to flip it over in other words and so we'll have c multiplied by h over binding energy. And so that's 2.998 times 10 to the 8 meters per second times 4.14 times 10 to the minus 15 electron volt seconds divided by 4.73 electron volts, the electron volts here cancel the seconds here cancel and we have an answer in meters. That's 2.6240 times 10 to the minus 7 meters and we'll convert that into nanometers just because that's a more traditional unit for wavelength of light so we multiply by 10 to the 9 nanometers for every meter. So that's 262 nanometers would be this longest possible wavelength that would still eject a photoelectron from silver and this is shorter than the lower limit of the visible range which is about 380 nanometers so this is ultraviolet light.