EM waves properties — speed, wavelength, frequency across the spectrum

Question

Arrange the electromagnetic spectrum in order of increasing frequency. State the speed, wavelength range, and one application of each type. How does energy relate to frequency?

(CBSE 12 & NEET — theory question with high weightage)

Solution — Step by Step

From lowest to highest frequency (longest to shortest wavelength):

Radio waves → Microwaves → Infrared → Visible light → Ultraviolet → X-rays → Gamma rays

Mnemonic: Ram Made Ice Very Unusual eXtra Good

All travel at $c = 3 \times 10^8$ m/s in vacuum
All are transverse waves ( $\vec{E} \perp \vec{B} \perp \vec{c}$ )
All obey $c = f\lambda$
All carry energy: $E = hf$ per photon
No medium needed for propagation

Type	Wavelength range	Frequency range	Application
Radio	$> 0.1$ m	$< 3 \times 10^9$ Hz	Broadcasting, communication
Microwave	1 mm – 0.1 m	$10^9 \text{--} 3 \times 10^{11}$ Hz	Oven, radar, satellite
Infrared	700 nm – 1 mm	$3 \times 10^{11} \text{--} 4.3 \times 10^{14}$ Hz	Night vision, remote control
Visible	400 – 700 nm	$4.3 \text{--} 7.5 \times 10^{14}$ Hz	Human vision, photography
Ultraviolet	10 – 400 nm	$7.5 \times 10^{14} \text{--} 3 \times 10^{16}$ Hz	Sterilisation, vitamin D
X-rays	0.01 – 10 nm	$3 \times 10^{16} \text{--} 3 \times 10^{19}$ Hz	Medical imaging, security
Gamma	$< 0.01$ nm	$> 3 \times 10^{19}$ Hz	Cancer treatment, nuclear physics

Why This Works

All EM waves are the same fundamental phenomenon — oscillating electric and magnetic fields propagating through space. They differ only in frequency (and therefore wavelength and energy). Higher frequency means shorter wavelength and more energy per photon.

graph LR
    A["Radio<br/>Lowest f<br/>Longest λ"] --> B["Microwave"]
    B --> C["Infrared"]
    C --> D["Visible<br/>400-700 nm"]
    D --> E["Ultraviolet"]
    E --> F["X-rays"]
    F --> G["Gamma<br/>Highest f<br/>Shortest λ"]
    H["Energy increases →"] -.-> G
    I["← Wavelength increases"] -.-> A

The energy relation $E = hf$ (where $h = 6.63 \times 10^{-34}$ J s is Planck’s constant) explains why gamma rays are dangerous (high energy per photon can ionise atoms) while radio waves are harmless (too low energy to break chemical bonds).

Alternative Method — Remember by Source

Each EM wave type has a characteristic source:

Radio: oscillating circuits
Microwave: klystron/magnetron
IR: hot bodies
Visible: very hot bodies, atoms
UV: sun, mercury lamps
X-rays: deceleration of fast electrons (Bremsstrahlung)
Gamma: nuclear transitions

For NEET: the most tested fact is that all EM waves travel at the same speed in vacuum. In a medium, different frequencies travel at different speeds (dispersion) — this is why a prism splits white light. But in vacuum, speed is always $c$ regardless of frequency.

Common Mistake

Students sometimes write that microwaves have the highest frequency or that radio waves have the shortest wavelength — getting the order backwards. Use the mnemonic and remember: frequency and wavelength are inversely related ( $c = f\lambda$ ). As frequency goes up, wavelength goes down. NEET 2023 had an ordering question that many students got wrong.

Question

Solution — Step by Step

Why This Works

Alternative Method — Remember by Source

Common Mistake

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