Matter Waves (Wave Particle Duality)

Special relativity said that

$E = pc$ if m=0

Plank said he could fit the Black Body radiation data assuming that that

$E= hf$ where $h = 6.63 \times 10^{-34} \mbox{ J} \cdot \mbox{s}$ = Plank's constant

Combining the two we have

$p=\frac{E}{c} = \frac{ h f}{c}$

$\Rightarrow$ photons have momentum like a particle (mv)

Do particles reciprocate and behave like photons?

De Broglie's Hypothesis

If photons can behave like particles by having momentum

Then can a particle behave like a wave by having wavelength

$p=\frac{ h f}{c} = \frac{h}{\lambda}$

or

$\lambda_{particle} = \frac{h}{p}=$ de Broglie Hypothesis

We know that X-rays having a wavelength of $\lambda_{X-rays} = 7.1 \times 10^{-11} \mbox{m}$ make an interference patter on an aluminum foil.

p_{X-ray} = \frac{h}{\lambda} = \frac{}{7.1 \times 10^{-11}}

Hit a crystal made of nickel with 54 eV electrons.

1.) 54 eV electrons

From hyperphysics: