# Question #d5082

Jan 10, 2017

The basis of the derivation is to equate two energy expressions:

$E = h \nu = \frac{h c}{\lambda}$

$E = m {c}^{2}$

Thus:

$m {c}^{2} = \frac{h c}{\lambda}$

$m c = \frac{h}{\lambda}$

$\lambda = \frac{h}{m c}$

To apply this equation to things moving at not the speed of light, but their own speed, de Broglie implicitly assumed that the moving object would have a measurable mass:

$\implies \textcolor{b l u e}{\lambda = \frac{h}{m v}}$

That, however, restricts the application to things with mass. i.e. you cannot use this equation for photons, but you can use it for electrons.

It does, however, say that things with considerable mass do have a wavelength... it is just immeasurably small. It gets reasonably large for quantum particles, like electrons and protons.