A photon and a nonrelativistic electron of mass m each have the same energy E. Find the ratio of their de Broglie wavelengths λₚₕₒₜₒₙ/λₑₗₑ꜀ₜᵣₒₙ (c is speed of light).
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Question

A photon and a nonrelativistic electron of mass m each have the same energy E. Find the ratio of their de Broglie wavelengths λₚₕₒₜₒₙ/λₑₗₑ꜀ₜᵣₒₙ (c is speed of light).

G1 Physics · Accepted Answer

Step 1: For a photon, E = pc = hc/λₚₕₒₜₒₙ, giving λₚₕₒₜₒₙ = hc/E. Step 2: For a nonrelativistic electron with kinetic energy E, E = p²/(2m), so p = √(2mE). Step 3: Electron de Broglie wavelength is λₑₗₑ꜀ₜᵣₒₙ = h/√(2mE). Step 4: Divide: λₚₕₒₜₒₙ/λₑₗₑ꜀ₜᵣₒₙ = (hc/E)/(h/√(2mE)). Step 5: Simplify: c√(2mE)/E = c√(2m/E). Final answer: c√(2m/E), Option C.