Lesson 9: Quantum Technologies | Modern Physics

Lesson at a Glance | He Tirohanga Whakamua

Do NowHow antimatter positron annihilation detects cancer tumors in PET scanners10 min

PET Scanner Physics

β^{+}

decay, matter-antimatter annihilation

e^{+} + e^{-} \to 2 γ

(

511 keV

)15 min

Solar Cells & TunnelingPhotovoltaic bandgap excitation (

h f & g t; E_{g}

) and flash memory quantum tunneling15 min

Portfolio EntryWrite Section 9: Modern Quantum & Medical Physics Technologies10 min

Exit DrillCalculate photon energy of a 511 keV PET gamma photon (

λ = 2.43 pm

)5 min

Ngā Whāinga Ako | Learning Intentions

Students will know

PET Medical Scanning: Radiotracer Fluorine-18 undergoes $β^{+}$ decay, emitting a positron ( $e^{+}$ ). Positron meets electron ( $e^{-}$ ), annihilating into two $511 keV$ gamma photons shot out at $180^{\circ}$ to conserve momentum.
Solar Photovoltaics: Sunlight photons ( $h f & g t; E_{g}$ ) promote valence electrons across the bandgap into the conduction band, driving electric current.
Quantum Tunneling: Electron wave functions ( $| ψ |^{2}$ ) penetrate potential energy barriers, enabling flash memory storage and scanning tunneling microscopy (STM).

Students will demonstrate

By calculating gamma photon frequency and wavelength for positron-electron annihilation ( $2 m_{e} c^{2} = 2 h f$ ).
By completing Section 9 of their Level 3 Modern Physics Mastery Portfolio.

Do Now | Tīmatanga Whakaaro (10 min)

Antimatter Medical Physics Prompt:

"PET hospital scanners use antimatter positrons inside the human body. Why does a positron-electron collision create TWO identical gamma rays shooting in exactly opposite directions ( $180^{\circ}$ )?"

Unpack: To conserve Linear Momentum ( $Σ {\vec{p}}_{i} = 0 \to {\vec{p}}_{γ 1} + {\vec{p}}_{γ 2} = 0$ ) and Mass-Energy ( $E = 2 m_{e} c^{2} \approx 1.022 MeV \to 2 \times 511 keV$ photons)! The 3D detector ring uses the exact timing of opposing photon strikes to map tumor positions to within millimeters.

Quantum & Nuclear Medical Applications (15 min)

1. PET Scan Annihilation Physics

$e^{+} + e^{-} \to γ_{1} + γ_{2}$
$E_{γ} = m_{e} c^{2} = 0.511 MeV = 8.18 \times 10^{- 14} J$
$λ = \frac{h c}{E_{γ}} = 2.43 \times 10^{- 12} m$ .

2. Solar Cell Bandgap Physics

Silicon bandgap $E_{g} = 1.1 eV$ . Incident photons must have $h f \geq E_{g}$ ( $λ \leq 1100 nm$ ) to excite electrons into the conduction band.

📁 Physics Modern Portfolio — Section 9: Quantum Technologies

Students open their Level 3 Physics Portfolio and complete Section 9:

Section 9 Requirements:

1. PET Scanner Physics Diagram: Draw a patient emitting pair-annihilation gamma rays into a circular 3D detector ring, detailing positron emission and momentum conservation.

2. Solar Photovoltaic Efficiency Solver: Calculate minimum photon frequency and maximum wavelength required to excite electrons across silicon ( $E_{g} = 1.1 eV$ ) and gallium arsenide ( $E_{g} = 1.4 eV$ ) bandgaps.

3. Excellence Quantum Tunneling Rationale: 1-paragraph explanation of how wave function barrier penetration enables solid-state drive (SSD) memory cells to trap charges without physical wear.

Exit Verification | Ka Mutu Hoki (5 min)

Exit Check:

"My Section 9 calculates PET annihilation photon energy E = 511 keV (lambda = 2.43 pm) and explains silicon solar bandgap photon excitation."

Teacher Planning & NCEA Alignment

NCEA Level 3 Physics Alignment (3 Credits Internal):

Applications of Modern Physics: Demonstrate understanding of application of physics concepts (photoelectric effect, binding energy, beta decay, relativity) to modern medical scanning, renewable solar technology, and quantum electronics.

Vocabulary: PET scan, positron annihilation ( $e^{+} + e^{-}$ ), gamma ray ( $511 keV$ ), bandgap ( $E_{g}$ ), semiconductor, quantum tunneling, wave function.

Other teaching approach: Guided Viewing & Problem Practice →

Lesson 9: Modern Quantum & Medical Physics Technologies