1. Hydrogen Spectrum in Astrophysics

The 656 nm H_α Balmer line is used to identify hydrogen in distant stars and nebulae. Red-shifted H_α indicates galaxies moving away from Earth (Hubble's law). The Lyman series absorption at 91.2 nm creates the Lyman break used to find very distant galaxies.

2. Electron Microscopy

de Broglie wavelength of electrons at 100 kV ≈ 0.004 Å — far smaller than X-ray wavelengths, allowing atomic-resolution imaging (TEM, SEM). This directly applies λ = h/√(2meV).

3. Photoelectric Sensors

Solar cells and photodetectors operate on the photoelectric effect. Semiconductor work functions determine which frequencies generate current. LED efficiency depends on energy gap (E = hν of emitted photon).

4. Atomic Emission Spectroscopy (AAS/OES)

Flame tests and emission spectrometers identify elements by their unique spectral lines (fingerprint). Each element has unique energy levels → unique spectral lines.

5. Laser Technology

Lasers use stimulated emission between specific energy levels. The wavelength is precisely determined by $\Delta E$ = hν. Ruby laser uses $Cr^{3+}$ energy levels; helium-neon uses Ne transitions.

6. Nuclear Medicine

Gamma rays from nuclear transitions (high-energy photons) follow E = hν. PET scans use 511 keV gamma photons from electron-positron annihilation.

7. Quantum Numbers in Chemistry

Quantum numbers explain:

• Periodic table structure (s, p, d, f blocks)
• Chemical bonding (orbital overlap)
• Magnetic properties (unpaired electrons → paramagnetism)
• Spectral splitting in magnetic fields (Zeeman effect)