De-Broglie equation for other particles except photon If E=hf is applicable for electron and other

Fescoisyncsibgyp8b

Fescoisyncsibgyp8b

Answered question

2022-05-13

De-Broglie equation for other particles except photon
If E=hf is applicable for electron and other particles, the De Broglie wavelength should be λ=hv/pc. Because, mc^2=hf which implies mc^2=hc/λ which implies m=h/λc and thus λ=hv/pc. But I have found in my text book that λ=h/p is applicable not only for photon but also for all particle. But how can λ=h/p=h/mv be applicable for all particle?

Answer & Explanation

Ari Jacobs

Ari Jacobs

Beginner2022-05-14Added 10 answers

The De Broglie relations
E = h ν , p = h λ
are applicable to all particles. However the relation between the frequency/energy and the wave length/momentum, is not the same. Thus, for photons f = c λ , for non-relativistic electrons E = p 2 2 m , for relativistic electrons E 2 = m 2 c 4 + p 2 c 2
quorums15lep

quorums15lep

Beginner2022-05-15Added 4 answers

For your last step you just introduce a v in both the numerator and denominator. That is meaningless as it is unity.
In the expression λ = h m c , you just have to set c = v to account for particles with different momenta and thus different velocities, not equal to the speed of light.
Do it in this way:
E = h f = m c 2
h c λ = m c 2
h λ = m c
λ = h m c
λ = h m v

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