Electromagnetic Spectrum 🌈
All electromagnetic waves zip through empty space at the same speed: \(c = 3 \times 10^{8}\,\text{m/s}\). From the longest wavelengths (radio) to the shortest (gamma), each band is set apart mostly by how we make and detect the waves rather than by any sharp boundary. :contentReference[oaicite:0]{index=0}
Snapshot of the Spectrum
- Order (long λ → short λ): Radio → Microwaves → Infrared → Visible → Ultraviolet → X-rays → Gamma-rays.
- Frequency range of visible light: \(4 \times 10^{14}\,\text{Hz} – 7 \times 10^{14}\,\text{Hz}\) (≈ 700 nm – 400 nm).
- There are no sharp “walls” between bands—neighbors overlap a bit.
Bands in Detail
📻 Radio Waves
- Made by accelerating charges in metal antennas.
- Typical frequencies: 500 kHz – 1 GHz.
- Handy numbers: AM 530 kHz – 1710 kHz, Short-wave up to 54 MHz, TV 54 MHz – 890 MHz, FM 88 MHz – 108 MHz, cell phones in the UHF slice.
- Main uses: broadcasting, TV, mobile communication.
📡 Microwaves
- Generated by special tubes (klystrons, magnetrons, Gunn diodes).
- Frequency in the gigahertz (GHz) range.
- Key uses: aircraft radar, speed guns, satellite links, and the microwave oven—its frequency matches water-molecule resonance for super-efficient heating 🍲!
🔥 Infrared (IR)
- Given off by hot objects and vibrating molecules.
- Often called heat waves because water, CO2, NH3 soak them up and warm up.
- Applications: physiotherapy lamps, remote controls, crop-growth imaging, greenhouse effect (keeps Earth cozy 🌍).
👁️ Visible Light
- The slice our eyes see: ≈ 700 nm – 400 nm.
- Different creatures “see” different bands—snakes sense IR; many insects extend into UV.
☀️ Ultraviolet (UV)
- Wavelengths: 400 nm → 0.6 nm.
- Main natural source: the Sun, but most UV is stopped by the ozone layer ~40–50 km up (hooray 🛡️).
- Uses: sterilizing water, LASIK eye surgery, detecting forged notes—but too much UV causes sunburn and eye damage, so welders wear dark goggles.
🩻 X-rays
- Made when high-energy electrons smash into a metal target.
- Wavelengths: 10 nm → 0.01 nm.
- Famous for medical imaging and treating some cancers—careful though, they can damage tissues.
💥 Gamma Rays
- Shortest wavelengths: < 0.01 nm.
- Born in nuclear reactions and radioactive decay.
- Penetrating enough to zap cancer cells in radiotherapy.
Handy Examples
Example 8.1 – Finding the Magnetic Field 🧭
For a wave with frequency \(25\,\text{MHz}\) traveling along the \(x\)-axis and electric field \(\mathbf{E}=6.3\,\hat{\jmath}\,\text{V m}^{-1}\):
\[ B \;=\; \frac{E}{c}\;=\;\frac{6.3}{3\times10^{8}}\;=\;2.1\times10^{-8}\,\text{T}, \] and it points in the \(+\hat{k}\) direction since \(\mathbf{E}\times\mathbf{B}\) must aim along \(+\hat{\imath}\). :contentReference[oaicite:1]{index=1}
Example 8.2 – Wavelength, Frequency & Electric Field 📝
Given \(B_y = (2 \times 10^{-7}) \sin\!\bigl(0.5 \times 10^{3}\,x + 1.5 \times 10^{11}\,t\bigr)\),
- \(\displaystyle \lambda = \frac{2\pi}{0.5\times10^{3}} = 1.26\,\text{cm}\).
- \(\displaystyle \nu = \frac{1.5\times10^{11}}{2\pi} \approx 23.9\,\text{GHz}\).
- The accompanying electric field (perpendicular to \(B\)) is \(E_z = 60 \sin(0.5\times10^{3}x + 1.5\times10^{11}t)\,\text{V m}^{-1}\).
Great practice for spotting \(k\), \(\omega\), and trusting \(E_0 = c B_0\)! 💡 :contentReference[oaicite:2]{index=2}
Production & Detection at a Glance
| Type | Typical λ Range | How It’s Produced | How We Spot It |
|---|---|---|---|
| Radio | >0.1 m | Rapid charge accelerations in antennas | Receiver aerials |
| Microwave | 0.1 m → 1 mm | Klystron / magnetron tubes | Point-contact diodes |
| Infrared | 1 mm → 700 nm | Vibrating atoms & molecules | Thermopile, bolometer, IR film |
| Visible | 700 nm → 400 nm | Electron jumps in atoms | Eyes, photocells, film |
| Ultraviolet | 400 nm → 1 nm | Inner-shell electron jumps | Photocells, film |
| X-ray | 1 nm → 0.001 nm | X-ray tubes, inner-shell transitions | Film, Geiger tubes |
| Gamma | <0.001 nm | Radioactive nuclear decay | Ionization chambers, film |
(Boundaries blur a little in real life.) :contentReference[oaicite:3]{index=3}
High-Yield NEET Nuggets 🏆
- Order & Ranges: Remember the spectrum sequence and the ball-park frequencies/wavelengths for quick MCQs.
- Speed Relation: For any electromagnetic wave, \( \dfrac{E}{B} = c \). Spot this in calculation-based questions.
- Microwave Resonance: Oven frequencies match water-molecule resonance—classic application favorite.
- Atmospheric Filters: Ozone stops most UV; greenhouse gases trap IR—popular conceptual hooks linking physics & environment.
- Medical Imaging: X-rays for diagnostics, gamma rays for cancer therapy—often paired in application-type problems.
