While the quantum model explains many physical processes that the classical model cannot, it must be consistent with those processes that the classical model does explain. Energy and momentum conservation are fundamental principles of classical physics. Use the Compton and photoelectric effects to explain how these conservation principles carry over to the quantum model of light.

Video Transcript

This is College Physics Answers with Shaun Dychko. In this question, we are meant to compare the classical concept of energy conservation to the quantum mechanical scenario of the photoelectric effect and we will also compare the idea of momentum being conserved in the classical context to the quantum mechanical context of quantum scattering. So the idea that a photon has an amount of energy equal to its frequency multiplied by Planck's constant— that's a quantum mechanical idea— and what's noticed when that photon hits an electron and ejects it from its atom, the electron will have a kinetic energy or maximum possible kinetic energy and if you add that to the binding energy of the electron in the atom that total will be the same as the energy of the photon and so in this sense the energy is conserved so in this quantum mechanical context, this is a confirmation that energy is still conserved. So now when we are talking about momentum, we have x-ray photons being scattered from electrons that are in an atom and these x-rays will turn into photons with a lower energy and therefore lower momentum after hitting the electrons and the amount by which their energy decreases and their momentum decreases is compensated for by an increase of an equal amount in the kinetic energy of the electron and the momentum of the electron so this confirms conservation of momentum and conservation of energy in this quantum mechanical context. And furthermore the idea that a photon can be thought of as a particle hitting another particle and momentum being conserved in this collision, this is quantum mechanical to say that a photon is a particle and so that's the way in which this scenario is quantum mechanical and in this scenario, we are seeing momentum and energy are conserved.