I have seen the equation for de Broglie wavelength derived through equating Einstein's $E=mc^{2}$, and Planck's $E=hf$, using a substitution from $c=f\lambda$ to make things in terms of wavelength. From this the following result is derived: $$ \lambda = \frac{h}{mc} $$ This makes sense to me under the assumption that such a wavelength exists. However, at this point a substitution is made for $c$ changing it to $v$. How is this valid? The speed of light is a specific velocity and in the case of Einstein's mass energy equivalence is important that it is such, and not just any velocity. Is there a good reason for this? And if not and this is just meant to be a dumbed down version to give to high school students, does anyone have a correct way of arriving at the desired result?



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