- $-0.90 \textrm{ eV}$
- Binding energy can not be negative.
- The kinetic energy of the electron should be less, or the wavelength of the photon should be much shorter.

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This is College Physics Answers with Shaun Dychko. Electrons ejected from a material allegedly have a kinetic energy of 4 electron volts given an incident photon wavelength of 400 nanometers. So we are gonna figure out what the binding energy is of this material based on equation [29.5] and we'll add binding energy to both sides and substract kinetic energy of the electron from both sides. So we have this; binding energy is Planck's constant times the frequency of the photon minus the kinetic energy of the electron. And we replace <i>f</i> with <i>c</i> over <i>λ</i> because that's the number that we are given and so we have <i>c</i> over <i>λ</i> here. So binding energy is Planck's constant times speed of light divided by wavelength minus the kinetic energy of the electron. So that's 1240 electron volt nanometers— this is from [29.14] in the textbook— divided by 400 nanometers gives us a term in units of electron volts minus the 4 electron volts of kinetic energy giving a binding energy of negative 0.90 electron volts. Now this is nonsensical because binding energies cannot be negative for a material that's stable. The kinetic energy of the electron should be less should be a smaller number so that it doesn't make this difference negative or the wavelength of the photon should be much shorter by and so having a smaller denominator here would make this term greater so that it would be greater than this term here. Either of those would make this number become positive for the binding energy which would be reasonable.