Lesson 2: Wave-Particle Duality | Modern Physics

Lesson at a Glance | He Tirohanga Whakamua

Do NowDo moving baseballs have a wavelength? Why don't they diffract?10 min

De Broglie EquationCalculating

λ = \frac{h}{p} = \frac{h}{m v}

for electrons vs macroscopic objects15 min

Electron DiffractionDavisson-Germer experiment & Transmission Electron Microscopy (TEM)15 min

Portfolio EntryWrite Section 2: Wave-Particle Duality & Matter Waves Guide10 min

Exit DrillCalculate de Broglie wavelength of an electron accelerated through 100V5 min

Ngā Whāinga Ako | Learning Intentions

Students will know

The De Broglie Hypothesis: All moving matter possesses a wave nature with wavelength $λ = \frac{h}{p} = \frac{h}{m v}$ .
Experimental evidence for matter waves: Electron Diffraction through a graphite crystal lattice creating circular interference rings.
Practical application: Transmission Electron Microscopy (TEM) achieves atomic-scale resolution ( $\approx 0.1 nm$ ) because electron wavelengths are $10^{5} \times$ shorter than visible light photons.

Students will demonstrate

By calculating de Broglie wavelengths for an electron ( $m_{e} = 9.11 \times 10^{- 31} kg$ ) vs a cricket ball ( $m = 0.16 kg$ ).
By completing Section 2 of their Level 3 Modern Physics Mastery Portfolio.

Do Now | Tīmatanga Whakaaro (10 min)

Macroscopic vs Microscopic Wavelength Prompt:

"If light (traditionally a wave) acts like a particle in the photoelectric effect, can electrons (traditionally particles) act like waves?"

Unpack: Yes! Louis de Broglie proposed symmetry in nature: $λ = \frac{h}{m v}$ . A 0.16kg cricket ball moving at $30 {ms}^{- 1}$ has $λ = 1.38 \times 10^{- 34} m$ (far smaller than an atomic nucleus, so zero observable diffraction occurs). But a fast electron has $λ \approx 1.2 \times 10^{- 10} m$ —the exact atomic spacing of graphite, causing clear wave interference!

De Broglie Wavelength & Electron Microscopy (15 min)

1. De Broglie Equation ( $λ = \frac{h}{p}$ )

$λ = \frac{h}{m v} = \frac{h}{\sqrt{2 m E_{k}}}$
As momentum ( $p = m v$ ) increases, de Broglie wavelength ( $λ$ ) decreases.

2. Electron Diffraction Evidence

Firing electrons through polycrystalline graphite produces concentric diffraction rings, proving matter exhibits wave interference ( $λ \approx d_{l a t t i c e}$ ).

📁 Physics Modern Portfolio — Section 2: Wave-Particle Duality

Students open their Level 3 Physics Portfolio and complete Section 2:

Section 2 Requirements:

1. Electron Diffraction Apparatus Diagram: Draw an electron gun, graphite target grid, and fluorescent screen showing concentric diffraction rings.

2. De Broglie Wavelength Solver: Calculate $λ$ for an electron accelerated through $150 V$ ( $E_{k} = 150 eV = 2.4 \times 10^{- 17} J$ ).

3. Excellence Electron Microscope Rationale: 1-paragraph explanation of why Transmission Electron Microscopes (TEM) resolve viral structures ( $10 nm$ ) that light microscopes cannot resolve due to diffraction limits ( $d \approx \frac{λ}{2}$ ).

Exit Verification | Ka Mutu Hoki (5 min)

Exit Check:

"My Section 2 calculates de Broglie wavelength lambda = 0.10 nm for a 150V electron, matching graphite atomic plane spacing and proving matter wave interference."

Teacher Planning & NCEA Alignment

NCEA Level 3 Physics Alignment (3 Credits Internal):

Wave-Particle Duality: Demonstrate understanding of de Broglie wavelength ( $λ = \frac{h}{p}$ ), matter waves, and diffraction.
Technology Applications: Explain resolving power in electron microscopy.

Vocabulary: Wave-particle duality, De Broglie wavelength ( $λ = \frac{h}{p}$ ), matter waves, electron diffraction, Davisson-Germer experiment, TEM microscope.

Other teaching approach: Guided Viewing & Problem Practice →

Lesson 2: Wave-Particle Duality & De Broglie Wavelength