Electromagnetic Spectrum – Global Overview

• Definition: The complete range of electromagnetic (EM) radiation, arranged by wavelength \lambda, frequency f, and photon energy E = hf.
• Canonical ordering (long \lambda → short \lambda):
  • Radio, Microwave, Infrared (IR), Visible, Ultraviolet (UV), X-ray, Gamma-ray.
• Representative quantitative scales (approx.):
  • Wavelengths: 10^3\ \text{m} \rightarrow 10^{-12}\ \text{m}.
  • Frequencies: 10^4\ \text{Hz} \rightarrow 10^{20}\ \text{Hz}.
• Characteristic object sizes that resonate with/compare to each band:
  • Buildings (radio), humans (microwave), honeybee (IR), pinpoint (visible), protozoans (UV), molecules/atoms/nuclei (X-ray/\gamma).
• Typical black-body temperatures of sources:
  • 1\ \text{K} (radio) → 10\ \text{M K} (gamma ray).
• Atmospheric transmission windows: radio and visible pass easily; most microwaves, parts of IR, UV-C, X-ray, and \gamma do not.

Radio Waves (AM, FM, Radar, MRI)

• AM (Amplitude Modulation)
  • Information encoded in wave amplitude.
  • Longer \lambda (hundreds of meters) ⇒ easily diffract around obstacles; large coverage area.
• FM (Frequency Modulation)
  • Information encoded in frequency deviation.
  • Shorter \lambda (~3 m); better audio fidelity; line-of-sight limitation.
• Radar = Radio Detection And Ranging
  • Sends out radio pulses & measures reflected signal delay and Doppler shift.
  • Police radar guns: outgoing wave vs. higher-frequency reflection from an approaching car → determines speed via \Delta f.
• MRI (Nuclear Magnetic Resonance Imaging)
  • Human tissue ≈ \text{H}_2\text{O} ⇒ many ^1\text{H} protons.
  • In a strong B-field, proton magnetic moments align; radio-frequency pulses tip them; relaxation emits detectable RF → 3-D tissue map.
  • Shows soft tissue contrast without ionizing radiation.

Microwaves

• Oven frequency chosen to match rotational resonances of water molecules → efficient heating if food contains water.
• Security/physics frontier: Terahertz (THz) detectors bridge microwaves & far-IR for imaging weapons, studying superconductors, etc.

Infrared Radiation

• Definition: 700\ \text{nm} \le \lambda \le 1\ \text{mm} (extends beyond visible red).
• Nearly all room-temperature thermal radiation peaks in IR.
• Applications:
  • Weather satellites: cloud-top temperatures mapped; color scales convert IR brightness to \deg\text{C} / \deg\text{F}.
  • Stinger missile seekers: track aircraft engine IR signature.
  • Infrared cameras (thermal imagers): operate out to \lambda \approx 14\,\mu\text{m}; visualize heat leaks, wildlife, medical inflammation.
• Centennial Light example: a ~110-year-old incandescent bulb (Livermore, CA) demonstrates low filament temperature & continuous IR-heavy output.

Black-Body & Thermal Laws (connects radio → \gamma)

• Black-body radiation: spectrum depends solely on absolute temperature T.
• Wien’s displacement law: \lambda_{\text{peak}} = \dfrac{3.0\times10^6\,\text{nm·K}}{T}.
  • Example: \lambda = 500\,\text{nm} \Rightarrow T = 6000\,\text{K} (solar surface).
  • Color trend: hotter ⇒ peak moves from red → blue.
• Stefan–Boltzmann law: P = \sigma A T^4 with \sigma = 5.68\times10^{-8}\ \text{W·m}^{-2}\text{K}^{-4}.
  • Sun: A = 6.0\times10^{18}\,\text{m}^2, T = 6000\,\text{K} ⇒ P \approx 4.4\times10^{26}\,\text{W}.
  • Halving T to 3000\,\text{K} drops P to 2.8\times10^{25}\,\text{W} (factor 16 reduction).
• Incandescent tungsten filament spectra plotted for TF=3400\,\text{K},3200\,\text{K} & TE=2850\,\text{K} vs. sunlight; most output in IR.

Ultraviolet (UV)

• Bands & biological impact:
  • UVA (320–400 nm): reaches ground most; aging, wrinkles; tanning beds.
  • UVB (280–320 nm): sunburn, cataracts, immune suppression.
  • UVC (≤280 nm): most energetic; absorbed by stratospheric ozone.
• DNA damage mechanism: UV photons break molecular bonds, causing mutations & skin cancer.
• Ozone & CFCs:
  • Chlorofluorocarbons (CFCs) – volatile \text{C}\text{l},\text{F} hydrocarbons (e.g., Freon). In stratosphere they release Cl radicals → catalytically destroy \text{O}_3 → thinning UV shield.
• Blacklights: emit long-wave UVA; fluorescence reveals bodily fluids, art pigments, security markings.

X-rays

• Range: 0.01\,\text{nm} \le \lambda \le 10\,\text{nm} ➔ f = 3\times10^{16}–3\times10^{19}\,\text{Hz}, E = 100–100\,\text{keV} per photon.
• Medical radiography: calcium-rich bone absorbs X‐rays; soft tissue transmits ⇒ image contrast.
• Backscatter X-ray scanners (airport security): detect reflected X-rays to reveal metallic/organic contraband under clothing; privacy concerns; optional use.
• Advanced imaging:
  • CT/CAT (Computed Tomography): rotating X-ray + computer reconstruction; ~500–700 mrem dose.
  • PET (Positron Emission Tomography): inject short-lived positron emitters (e.g., ^{18}\text{F}, ^{11}\text{C}). Coincident \gamma photons at 511\,\text{keV} map glucose uptake (cancer, brain activity); ~1000 mrem.
  • MRI & MRA noted for complementary non-ionizing soft-tissue and vascular imaging; comparison chart:
  • X-ray: bony detail only.
  • CT: fast, moderate detail, bleeds/masses.
  • MRI: slow, high detail, minor lesions.
  • MRA: blood-flow mapping.
  • PET: metabolic activity, cancer hotspots.

Gamma Rays (\gamma-rays)

• Highest frequency, f \gtrsim 10^{19}\,\text{Hz}; extremely penetrating & ionizing.
• Produced by nuclear transitions (gamma decay) and astrophysical events (gamma-ray bursts).
• Hazard: low chronic exposure manageable, but intense bursts are lethal (massive cellular ionization).

Non-EM Bonus: Ultrasound

• Definition: mechanical pressure waves with f > 20\,\text{kHz} (beyond human hearing); medical imaging typically 2–15\,\text{MHz}.
• Not part of EM spectrum, but shares imaging applications: fetal scans, blood-flow Doppler, industrial flaw detection.

Key Mathematical & Physical Takeaways

• E = hf = \dfrac{hc}{\lambda} links photon energy to \lambda.
• Atmospheric opacity determines astronomical instrument placement (Earth vs. satellite).
• Resonance (water rotation for microwaves, molecular vibrations for IR) governs selective energy absorption.
• Ionizing vs. non-ionizing boundary sits in UV; health regulations scale with photon energy and dose.
• Imaging trade-offs (resolution, contrast, safety, cost) dictate modality choice in medicine and security.