Electromagnetic Spectrum and Wave Properties

Master the complete EM spectrum from radio waves to gamma rays for JEE

13 min read

Electromagnetic Spectrum and Wave Properties

Real-Life Hook

Your daily life is bathed in electromagnetic waves! Right now, radio waves carry music to your car, microwaves heat your food, infrared radiation from your TV remote changes channels, visible light lets you read this, UV rays from the sun give you a tan (and sunburn!), X-rays at the dentist reveal cavities, and cosmic gamma rays from space bombard Earth constantly. All these are the SAME phenomenon - electromagnetic waves - just at different frequencies! The microwave in your kitchen operates at 2.45 GHz (same frequency as WiFi!) to make water molecules vibrate and heat food, while your skin feels infrared as warmth from a fireplace. Understanding the EM spectrum explains everything from why the sky is blue to how night-vision goggles work!

The Electromagnetic Spectrum

Complete Spectrum Overview

Electromagnetic waves span an enormous range of frequencies and wavelengths:

EM Spectrum Range

  • Frequency: 10⁴ Hz (radio) to 10²² Hz (gamma rays)
  • Wavelength: 10⁴ m (radio) to 10⁻¹⁴ m (gamma rays)
  • All travel at speed of light: c = 3 × 10⁸ m/s in vacuum

Fundamental Relation:

$$c = f\lambda = 3 \times 10^8 \text{ m/s}$$

where f = frequency, λ = wavelength

The Seven Main Regions

TypeWavelength RangeFrequency RangeEnergySource
Radio> 0.1 m< 3 GHzLowestOscillating circuits
Microwave1 mm - 0.1 m3 GHz - 300 GHzVery lowMagnetron, klystron
Infrared700 nm - 1 mm300 GHz - 4×10¹⁴ HzLowHot objects, atoms
Visible400 nm - 700 nm4×10¹⁴ - 7.5×10¹⁴ HzModerateAtoms, molecules
Ultraviolet10 nm - 400 nm7.5×10¹⁴ - 3×10¹⁶ HzHighHot objects, atoms
X-rays0.01 nm - 10 nm3×10¹⁶ - 3×10¹⁹ HzVery highInner shell electrons
Gamma rays< 0.01 nm> 3×10¹⁹ HzHighestNuclei, cosmic sources

Memory Aid: Roy Made India Very Unique Xceptionally Great

  • Radio, Microwave, Infrared, Visible, Ultraviolet, X-rays, Gamma rays

Detailed Properties of Each Region

1. Radio Waves (λ > 0.1 m)

Characteristics:

  • Longest wavelength, lowest frequency
  • Can travel long distances
  • Reflect from ionosphere (AM waves)
  • Penetrate buildings and fog

Production:

  • Rapidly oscillating currents in antennas
  • LC oscillator circuits
  • Transmitters with electron oscillations

Applications:

  • AM radio: 530-1600 kHz (λ ~ 200-500 m)
  • FM radio: 88-108 MHz (λ ~ 3 m)
  • TV broadcasting: 54-890 MHz
  • Cell phones: 800-2000 MHz
  • Radar: 1-40 GHz

Detection: Antenna + tuned circuit (LC resonance)

Penetration: High (through walls, fog)

Biological Effect: Minimal at low power

2. Microwaves (1 mm - 0.1 m)

Characteristics:

  • Wavelength: 1 mm to 30 cm
  • Absorbed by water molecules
  • Line-of-sight propagation
  • Used in satellite communication

Production:

  • Magnetron (microwave oven)
  • Klystron valve
  • Gunn diode

Applications:

  • Microwave ovens: 2.45 GHz (λ = 12.2 cm)
  • WiFi: 2.4 GHz and 5 GHz
  • Radar (Radio Detection And Ranging)
  • Satellite communication: 1-40 GHz
  • Speed detection (police radar guns)

Detection: Point-contact diodes, horn antennas

Mechanism in Microwave Oven:

  • Water molecules are polar (H₂O)
  • Microwaves cause rotational oscillation
  • Friction generates heat
  • Frequency 2.45 GHz matches water resonance

Biological Effect: Heating effect (can cook tissue!)

3. Infrared (IR) Waves (700 nm - 1 mm)

Characteristics:

  • Felt as heat
  • Emitted by all warm objects
  • Three sub-regions: Near-IR, Mid-IR, Far-IR

Production:

  • Hot bodies (thermal radiation)
  • Infrared LEDs and lasers
  • Molecular vibrations

Applications:

  • Remote controls: Near-IR (~ 940 nm)
  • Night vision devices (thermal imaging)
  • Infrared photography
  • Heat lamps (physiotherapy)
  • Greenhouse effect (traps Earth’s heat)
  • Infrared spectroscopy (molecular identification)
  • Motion sensors

Detection:

  • Thermopile, bolometer
  • Photodiodes (InGaAs, InSb)
  • Thermal cameras

Fun Fact: Your body emits ~100 W of infrared radiation!

Biological Effect: Warming, can cause skin burns at high intensity

4. Visible Light (400 nm - 700 nm)

Characteristics:

  • Only EM waves visible to human eye
  • Seven colors: VIBGYOR
  • Responsible for photosynthesis

Wavelength Ranges:

  • Violet: 400-450 nm (highest frequency)
  • Indigo: 450-475 nm
  • Blue: 475-495 nm
  • Green: 495-570 nm
  • Yellow: 570-590 nm
  • Orange: 590-620 nm
  • Red: 620-700 nm (lowest frequency)

Production:

  • Atomic transitions (outer electrons)
  • Incandescent bulbs (hot filament)
  • LEDs (semiconductor junctions)
  • Fluorescent lamps, lasers

Applications:

  • Vision, photography
  • Optical fiber communication
  • Photosynthesis (plants use red and blue)
  • Laser technology
  • Holography

Detection: Eye (retina - rods and cones), photographic film, CCD sensors

Energy: E = hf where h = Planck’s constant

  • Violet: highest energy (~3 eV)
  • Red: lowest energy (~1.8 eV)

Why Sky is Blue?: Rayleigh scattering (∝ 1/λ⁴) scatters blue light more than red

5. Ultraviolet (UV) Rays (10 nm - 400 nm)

Characteristics:

  • Higher energy than visible light
  • Most UV from sun blocked by ozone layer
  • Can cause chemical reactions

Sub-regions:

  • UV-A (315-400 nm): Tanning, aging
  • UV-B (280-315 nm): Sunburn, vitamin D
  • UV-C (100-280 nm): Germicidal (blocked by ozone)

Production:

  • Sun (main natural source)
  • Mercury vapor lamps
  • Welding arcs
  • Inner shell electron transitions

Applications:

  • Sterilization (UV-C kills bacteria/viruses)
  • Fluorescence (black light, security markers)
  • Vitamin D synthesis in skin
  • EPROM erasing
  • Photolithography (chip manufacturing)
  • Forensics (detecting bodily fluids)

Detection:

  • Photographic plates
  • Fluorescent materials
  • Photomultiplier tubes

Biological Effects:

  • Positive: Vitamin D production, kills germs
  • Negative: Sunburn, skin cancer, eye damage (cataracts)
  • Damages DNA (causes mutations)

Protection: Sunscreen, ozone layer, sunglasses

6. X-rays (0.01 nm - 10 nm)

Characteristics:

  • High penetrating power
  • Ionizing radiation
  • Stopped by heavy elements (lead, bone)

Production:

  • X-ray tube: High-energy electrons hit metal target
  • Inner shell electron transitions
  • Bremsstrahlung (braking radiation)

Typical X-ray Tube:

  • Cathode emits electrons (thermionic emission)
  • High voltage (~50 kV) accelerates electrons
  • Electrons hit tungsten anode
  • X-rays emitted (1% energy, 99% heat!)

Applications:

  • Medical imaging (radiography, CT scans)
  • Cancer treatment (radiotherapy)
  • Airport security scanners
  • X-ray crystallography (DNA structure discovered this way!)
  • Industrial inspection (weld testing, cracks)
  • Astronomical observations (X-ray telescopes)

Types:

  • Soft X-rays: Lower energy, less penetrating
  • Hard X-rays: Higher energy, more penetrating

Detection:

  • Photographic film
  • Scintillation counters
  • Solid-state detectors

Biological Effects:

  • Ionizing radiation
  • Damages cells and DNA
  • Cancer risk with high exposure
  • Used in controlled doses for therapy

Safety: Lead aprons, minimal exposure time

7. Gamma (γ) Rays (λ < 0.01 nm)

Characteristics:

  • Shortest wavelength, highest frequency
  • Highest energy photons
  • Highest penetrating power
  • Extremely dangerous

Production:

  • Radioactive decay (nuclear transitions)
  • Nuclear reactions (fission, fusion)
  • Cosmic sources (supernovae, pulsars, black holes)
  • Particle-antiparticle annihilation

Energy: MeV (million electron volts) range

Applications:

  • Cancer treatment (radiotherapy - kills cancer cells)
  • Food irradiation (sterilization, preservation)
  • Gamma knife surgery (brain surgery without incision)
  • Industrial gauging (thickness measurement)
  • Astronomy (studying cosmic events)
  • Sterilization of medical equipment

Detection:

  • Geiger-Müller counter
  • Scintillation detectors
  • Semiconductor detectors

Biological Effects:

  • Most dangerous radiation
  • Destroys living cells
  • Causes mutations, cancer
  • Radiation sickness at high doses

Shielding: Thick lead or concrete required

Fun Fact: Gamma-ray bursts from space are the most energetic events in the universe!

Comparison Table: Key Differences

PropertyRadioMicrowaveIRVisibleUVX-rayGamma
WavelengthLargestLargeMediumSmallSmallerVery smallSmallest
FrequencyLowestLowMediumMedium-highHighVery highHighest
EnergyLowestLowMediumMediumHighVery highHighest
PenetrationHighMediumLowVery lowLowHighVery high
Ionizing?NoNoNoNoPartiallyYesYes
DangerMinimalLowLowNoneMediumHighVery high
Common UseCommunicationCooking, WiFiHeatingVisionSterilizationMedical imagingCancer therapy

Energy of Photons

Photon Energy

$$E = hf = \frac{hc}{\lambda}$$

Where:

  • h = Planck’s constant = 6.626 × 10⁻³⁴ J·s
  • f = frequency (Hz)
  • λ = wavelength (m)
  • c = speed of light = 3 × 10⁸ m/s

Alternative form (when energy in eV):

$$E(\text{eV}) = \frac{1240}{\lambda(\text{nm})}$$

Examples:

  • Red light (620 nm): E = 2 eV
  • Blue light (450 nm): E = 2.76 eV
  • UV (300 nm): E = 4.13 eV
  • X-ray (1 nm): E = 1240 eV = 1.24 keV
  • Gamma ray (0.01 nm): E = 124 keV

Memory Tricks

“RMIVUXG” for EM Spectrum Order

Radio → Microwave → Infrared → Visible → Ultraviolet → X-rays → Gamma rays

Or: “Real Men In Vegas Usually X-ray Gorillas”

Wavelength-Frequency Inverse Relation

“Wavelength Downs, Frequency Ups”

  • Long wavelength → Low frequency (radio)
  • Short wavelength → High frequency (gamma)

Energy Increases with Frequency

“Frequency Up, Energy Up”

  • E = hf (direct proportion)
  • Radio: lowest energy
  • Gamma: highest energy

Visible Spectrum: “VIBGYOR”

Violet → Indigo → Blue → Green → Yellow → Orange → Red

Or: “Very Intelligent Boys Get Yellow Oranges Readily”

Wavelength order: Violet shortest (~400 nm), Red longest (~700 nm)

Ionizing vs Non-ionizing

“UV and Beyond - Ionizing”

  • Radio, Microwave, IR, Visible: Non-ionizing (safe)
  • UV (partially), X-ray, Gamma: Ionizing (dangerous)

Applications Mnemonic

  • Radio: Radio/TV
  • Microwave: Microwave oven
  • IR: Infrared remote
  • Visible: Vision
  • UV: Ultraviolet sterilization
  • X-ray: X-ray imaging
  • Gamma: Gamma knife surgery

Common Unit Conversion Mistakes

Wavelength Units

  • Meter (m): Radio waves (km to m)
  • Centimeter (cm): Microwaves
  • Micrometer (μm): Infrared
  • Nanometer (nm): Visible, UV, X-rays (1 nm = 10⁻⁹ m)
  • Angstrom (Å): X-rays, gamma rays (1 Å = 10⁻¹⁰ m = 0.1 nm)

Common Error: Mixing nm and Å

  • 10 nm = 100 Å
  • X-ray: 1 Å = 0.1 nm (NOT 1 nm!)

Frequency Units

  • Hertz (Hz): Base unit
  • Kilohertz (kHz): 10³ Hz (AM radio)
  • Megahertz (MHz): 10⁶ Hz (FM radio, TV)
  • Gigahertz (GHz): 10⁹ Hz (Microwave, WiFi)
  • Terahertz (THz): 10¹² Hz (IR)

Quick Conversions:

  • 1 GHz = 1000 MHz = 10⁹ Hz
  • WiFi 2.4 GHz = 2.4 × 10⁹ Hz

Energy Units

  • Joule (J): SI unit
  • Electron volt (eV): 1 eV = 1.6 × 10⁻¹⁹ J
  • keV: 10³ eV (X-rays)
  • MeV: 10⁶ eV (Gamma rays)

Shortcut for visible light:

$$E(\text{eV}) = \frac{1240}{\lambda(\text{nm})}$$

Example: 620 nm red light → E = 1240/620 = 2 eV

Speed of Light

  • c = 3 × 10⁸ m/s in vacuum
  • Slightly slower in media (air ≈ 3 × 10⁸ m/s, water ≈ 2.25 × 10⁸ m/s)

For calculations: Use c = 3 × 10⁸ m/s unless told otherwise

Interactive Demo: Visualize EM Spectrum Waves

Explore how different frequencies create waves across the electromagnetic spectrum.

Important Formulas

Wave Relation

$$c = f\lambda$$ $$f = \frac{c}{\lambda}, \quad \lambda = \frac{c}{f}$$

Photon Energy

$$E = hf = \frac{hc}{\lambda}$$

Energy in eV (for wavelength in nm)

$$E(\text{eV}) = \frac{1240}{\lambda(\text{nm})}$$

Momentum of Photon

$$p = \frac{E}{c} = \frac{h}{\lambda}$$

3-Level Practice Problems

Level 1: JEE Main Basics

Problem 1: Calculate the frequency of red light with wavelength 700 nm. (c = 3 × 10⁸ m/s)

Solution

Given:

  • λ = 700 nm = 700 × 10⁻⁹ m = 7 × 10⁻⁷ m

Using: $c = f\lambda$

$$f = \frac{c}{\lambda} = \frac{3 \times 10^8}{7 \times 10^{-7}}$$ $$f = \frac{3}{7} \times 10^{15} = 4.29 \times 10^{14} \text{ Hz}$$

Answer: f = 4.3 × 10¹⁴ Hz (in visible range ✓)

Problem 2: A radio station broadcasts at 100 MHz. Find the wavelength of the radio waves. (c = 3 × 10⁸ m/s)

Solution

Given:

  • f = 100 MHz = 100 × 10⁶ Hz = 10⁸ Hz

Using: $\lambda = \frac{c}{f}$

$$\lambda = \frac{3 \times 10^8}{10^8} = 3 \text{ m}$$

Answer: λ = 3 m (typical FM radio wavelength ✓)

Level 2: JEE Main Advanced

Problem 3: Calculate the energy of a photon of UV light with wavelength 300 nm in both Joules and electron volts. (h = 6.626 × 10⁻³⁴ J·s, c = 3 × 10⁸ m/s, 1 eV = 1.6 × 10⁻¹⁹ J)

Solution

Given:

  • λ = 300 nm = 300 × 10⁻⁹ m = 3 × 10⁻⁷ m

Energy in Joules:

$$E = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{3 \times 10^{-7}}$$ $$E = \frac{19.878 \times 10^{-26}}{3 \times 10^{-7}} = 6.626 \times 10^{-19} \text{ J}$$

Energy in eV:

$$E = \frac{6.626 \times 10^{-19}}{1.6 \times 10^{-19}} = 4.14 \text{ eV}$$

Or using shortcut:

$$E(\text{eV}) = \frac{1240}{300} = 4.13 \text{ eV}$$

Answer:

  • E = 6.63 × 10⁻¹⁹ J
  • E = 4.14 eV

Note: This UV photon has enough energy to break chemical bonds!

Problem 4: Microwaves of frequency 2.45 GHz are used in microwave ovens. Calculate: (a) Wavelength (b) Energy per photon in eV

Solution

Given:

  • f = 2.45 GHz = 2.45 × 10⁹ Hz

(a) Wavelength:

$$\lambda = \frac{c}{f} = \frac{3 \times 10^8}{2.45 \times 10^9}$$ $$\lambda = 1.224 \times 10^{-1} \text{ m} = 12.24 \text{ cm}$$

(b) Energy:

$$E = hf = 6.626 \times 10^{-34} \times 2.45 \times 10^9$$ $$E = 1.62 \times 10^{-24} \text{ J}$$

In eV:

$$E = \frac{1.62 \times 10^{-24}}{1.6 \times 10^{-19}} = 1.01 \times 10^{-5} \text{ eV}$$ $$E \approx 10 \text{ μeV}$$

Answer:

  • (a) λ = 12.2 cm
  • (b) E = 10 μeV (very low energy!)

Physical Insight: Individual microwave photons have tiny energy, but billions of them heat food effectively!

Level 3: JEE Advanced

Problem 5: An X-ray tube operates at 50 kV. Assuming all kinetic energy of electrons is converted to X-ray photons, calculate: (a) Minimum wavelength of X-rays produced (b) Maximum frequency (Use h = 6.626 × 10⁻³⁴ J·s, e = 1.6 × 10⁻¹⁹ C, c = 3 × 10⁸ m/s)

Solution

Given:

  • V = 50 kV = 50,000 V

Maximum energy of X-ray photon = KE of electron:

$$E_{max} = eV = 1.6 \times 10^{-19} \times 50,000$$ $$E_{max} = 8 \times 10^{-15} \text{ J}$$

Or: $E_{max} = 50$ keV

(a) Minimum wavelength (highest energy → shortest λ):

$$\lambda_{min} = \frac{hc}{E_{max}} = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{8 \times 10^{-15}}$$ $$\lambda_{min} = \frac{19.878 \times 10^{-26}}{8 \times 10^{-15}} = 2.48 \times 10^{-11} \text{ m}$$ $$\lambda_{min} = 0.248 \text{ Å} = 0.0248 \text{ nm}$$

(b) Maximum frequency:

$$f_{max} = \frac{c}{\lambda_{min}} = \frac{3 \times 10^8}{2.48 \times 10^{-11}}$$ $$f_{max} = 1.21 \times 10^{19} \text{ Hz}$$

Answer:

  • (a) λ_min = 0.248 Å or 0.025 nm
  • (b) f_max = 1.21 × 10¹⁹ Hz

Physical Meaning: This is the “cut-off wavelength” - minimum possible λ for this X-ray tube.

Problem 6: The wavelength of gamma rays is 10⁻¹² m, and that of radio waves is 10⁴ m. Find the ratio of: (a) Their frequencies (b) Their photon energies

Solution

Given:

  • λ_gamma = 10⁻¹² m
  • λ_radio = 10⁴ m

(a) Frequency ratio:

Since $f = \frac{c}{\lambda}$:

$$\frac{f_{gamma}}{f_{radio}} = \frac{c/\lambda_{gamma}}{c/\lambda_{radio}} = \frac{\lambda_{radio}}{\lambda_{gamma}}$$ $$\frac{f_{gamma}}{f_{radio}} = \frac{10^4}{10^{-12}} = 10^{16}$$

(b) Energy ratio:

Since $E = hf \propto f$:

$$\frac{E_{gamma}}{E_{radio}} = \frac{f_{gamma}}{f_{radio}} = 10^{16}$$

Or directly using $E = \frac{hc}{\lambda}$:

$$\frac{E_{gamma}}{E_{radio}} = \frac{\lambda_{radio}}{\lambda_{gamma}} = \frac{10^4}{10^{-12}} = 10^{16}$$

Answer:

  • (a) f_gamma/f_radio = 10¹⁶ (gamma rays have 10¹⁶ times higher frequency!)
  • (b) E_gamma/E_radio = 10¹⁶ (gamma photons are 10¹⁶ times more energetic!)

Physical Insight: This huge range shows the incredible span of the EM spectrum!

Key Takeaways

  1. All EM waves travel at speed c = 3 × 10⁸ m/s in vacuum
  2. c = fλ is the fundamental relation (inverse relation between f and λ)
  3. Energy increases with frequency: E = hf
  4. Seven main regions: Radio → Microwave → IR → Visible → UV → X-ray → Gamma
  5. Ionizing radiation: UV (partially), X-rays, Gamma rays (dangerous!)
  6. Applications: Each region has unique uses based on its properties
  7. Spectrum is continuous: No sharp boundaries between regions

Exam Tips

  • JEE Main: Focus on calculating f, λ, E; know applications of each region
  • JEE Advanced: Expect conceptual questions, energy calculations, and comparisons
  • Common trap: Unit errors (nm vs Å, MHz vs GHz) - always convert to SI!
  • Quick recall: E(eV) = 1240/λ(nm) for visible/UV calculations
  • Conceptual: Understand why different waves have different applications
  • Order matters: Know the sequence from low to high energy/frequency
  • Real-world: Link each wave type to daily applications (helps memory!)

Last updated: March 8, 2025