The relationship between momentum and energy from Einstein’s theory of relativity is E² - (pc)² = E₀², where, in this context, E₀ = mc² is the rest energy rather than the work function.

a. A photon is a massless particle. What is a photon’s momentum p in terms of its energy E?

b. Einstein also claimed that the energy of a photon is related to its frequency by E = hf. Use this and your result from part a to write an expression for the wavelength l of a photon in terms of its momentum p.

c. Your result for part b is for a “particle-like wave.” Suppose you thought this expression should also apply to a “wave-like particle.” What is your expression for l if you replace p with the classical mechanics expression for the momentum of a particle of mass m? Is this a familiar-looking expression?