Question

As far as energy band diagrams (E-k) of solid crystals are concerned, the photon in the spectrum is a particle that carries Eₚₕₒₜₒₙ= hv/λ and a momentum p=hv(k = 2π/λ) that is negligible as compared to that of the electrons in the solid crystal. Explain

why the latter is true.

Answer 1

The photon's momentum is negligible compared to electrons because photons are massless and their momentum, even though existent, is much smaller than that of the more massive electrons that significantly influence the energy levels in solid crystals.

Step-by-step explanation:

The student's question revolves around the comparison of momentum between photons and electrons in the context of energy band diagrams of solid crystals. The reason why the photon's momentum is negligible compared to that of electrons is due to the differences in their respective masses. Photons, being massless particles, have a momentum given by p = hν(k = 2π/λ), where h is Planck's constant, ν is the frequency, and λ is the wavelength. This formula shows that even though photons have momentum, it is significantly smaller than the momentum of electrons, which have mass and can be described by relativistic momentum mu. In solid-state physics, when solving Schrödinger's equation for the periodic potential in a crystal, the impact of the electron's momentum is substantial in determining the energy levels, while the photon's momentum can often be neglected.