Hi, I got the following question in my textbook: [translated]"Compare the wavelength of a photon and an electron where the photon and the electron have the same momentum".(adsbygoogle = window.adsbygoogle || []).push({});

My thinking is the following:

Firstly, p_{p}(photon) = p_{e}(electron).

My textbook briefly mentions the extention of the mass-energy equivalence E^{2}= p^{2}c^{2}+ m^{2}c^{4}, so I go by this since the particles have different speeds. The de Broglie wavelength of the electron is given by f_{e}= E/h = √(p^{2}c^{2}+ m^{2}c^{4}) / h. The wavelength of the photon is the same except that the mass is 0, so it reduces to f_{p}= √(p^{2}c^{2}) / h. Since m^{2}c^{4}≥ 0 it follows that f_{e}≥ f_{p}.

My textbook says that the answer is that f_{e}= f_{p}tho. Their argument is that p = h/λ holds for both the electron and the photon. But they previously state that it only applies for massless particles. They derive it from E^{2}= p^{2}c^{2}+ m^{2}c^{4}by setting m to 0. [translated]"[...]E = pc which holds for massless particles.[...] we find that p=h/λ".

Why is my argument invalid and why does λ=h/p hold for the electron? Thanks!

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# Why is deBroglie λ for electrons the same as λ for photons?

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