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I recently came across a proof for the De Broglie wave equation in a book, which went as follows:

E of photon = mc2

= m*c*c

= (m*c)c

= (p)c ( ie - momentum*speed of light)

= (p)(f*lamda)

Therefore, hf = p(f*lambda)

Therefore, p = hf/ f*lambda

= h/lambda.

Therefore, Lambda (ie- wavelength) = h/ mv.

However, I'm not sure if I agree with this, so I wanted to ask a few questions. Firstly, it is true that the energy of a photon = hf, but I dont think that it should equal mc2. After all, this Einsteinian equation literally means energy produce = mass destroyed*speed of light. So, what mass has been destroyed to create the energy of the photon? Furthermore, how can we take mc to be the momentum of the photon, if this is mass destroyed, not mass of the photon?

As slightly different question, what exactly is the wavelength of a particle? If the wavelength of a wave is "the distance between two crests or adjacent points", then what is the wavelength of a particle?

Thanks is advance. :-D

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# The De Broglie Wave Equation

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