Problem 3
Monochromatic light in vacuum has frequency f and wavelength λ. A light photon is described using Planck’s constant h and the speed of light c=3.00×10⁸ m/s; ignore interactions with matter. (a) Relate f and λ through wave propagation. (b) Derive one photon’s energy E_γ in terms of f and then λ. (c) Find momentum magnitude p_γ and check dimensions of E_γ and p_γ. Use SI units throughout and treat components as ideal exactly as specified. State sign conventions when writing equations and retain units in final results.
problems.proof.stepOf
problems.proof.analysis
Insert the intermediate result into the relevant definition or equation to obtain the final expression. Checking signs and limits catches a wrong branch or omitted constraint.