Dual Nature — Matter Waves (de Broglie) (Medium)

Quick Recap — Matter Waves (de Broglie)

• de Broglie wavelength: $\lambda=\dfrac{h}{p}=\dfrac{h}{mv}=\dfrac{h}{\sqrt{2m\,KE}}=\dfrac{h}{\sqrt{2mqV}}$.
• Electron shortcut: $\lambda=\dfrac{12.27}{\sqrt{V}}$ Å (with $V$ in volts).
• Trends: $\lambda\propto\dfrac{1}{p}$, so heavier or faster particles have shorter wavelengths; macroscopic objects have immeasurably tiny $\lambda$.
• Confirmation: the Davisson–Germer experiment (electron diffraction) verified the wave nature of matter. In a Bohr orbit, $2\pi r_n=n\lambda$.

Worked mini-example. An electron accelerated through 100 V has $\lambda=\dfrac{12.27}{\sqrt{100}}=1.23$ Å — comparable to atomic spacings, hence electron diffraction.