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

Question

Arrange the following electromagnetic waves in order of increasing frequency: microwaves, gamma rays, visible light, X-rays, radio waves, infrared, ultraviolet. Also state which has the longest wavelength and the highest energy.

Solution — Step by Step

The electromagnetic spectrum, from lowest frequency (longest wavelength) to highest frequency (shortest wavelength):

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

All EM waves travel at the same speed in vacuum: $c = 3 \times 10^8$ m/s.

Since $c = \nu\lambda$ , frequency and wavelength are inversely related for all EM waves.

Longest wavelength: Radio waves (can be km long)
Shortest wavelength: Gamma rays (less than $10^{-12}$ m)
Highest energy: Gamma rays, because $E = h\nu$ and they have the highest frequency

\text{Radio} < \text{Microwave} < \text{Infrared} < \text{Visible} < \text{UV} < \text{X-rays} < \text{Gamma rays}

Radio waves have the longest wavelength. Gamma rays have the highest energy.

Why This Works

All electromagnetic waves are produced by accelerating charges and consist of oscillating electric and magnetic fields perpendicular to each other and to the direction of propagation. The only difference between radio waves and gamma rays is their frequency (and therefore wavelength and energy).

graph LR
    A["Radio Waves"] --> B["Microwaves"]
    B --> C["Infrared"]
    C --> D["Visible Light"]
    D --> E["Ultraviolet"]
    E --> F["X-rays"]
    F --> G["Gamma Rays"]
    style A fill:#ff9999
    style G fill:#9999ff

The key relations that connect everything:

c = \nu\lambda \quad \text{and} \quad E = h\nu = \frac{hc}{\lambda}

Higher frequency means shorter wavelength means more energy per photon. This is why gamma rays are dangerous — each photon carries enough energy to ionise atoms and break chemical bonds.

NEET and CBSE boards love asking about specific EM wave properties: which wave is used in radar (microwave), which causes sunburn (UV), which is used in night-vision cameras (infrared). Memorise the applications alongside the spectrum order.

Alternative Method

Use the mnemonic Real Men Invest Very Unusual aXes Generously — Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma. This gives you the order from low to high frequency. For wavelength order, just reverse it.

For numerical problems, remember: visible light spans approximately $400$ nm (violet) to $700$ nm (red). Anything shorter is UV/X-ray/gamma; anything longer is IR/microwave/radio.

Common Mistake

Thinking different EM waves travel at different speeds in vacuum. All EM waves travel at $c = 3 \times 10^8$ m/s in vacuum regardless of frequency. The speed changes only when they enter a medium — and different frequencies refract differently (that is how a prism splits white light). In vacuum, speed is universal. This distinction between “in vacuum” and “in medium” is tested frequently in CBSE board exams.

c = \nu\lambda = 3 \times 10^8 \text{ m/s (in vacuum)}

E = h\nu = \frac{hc}{\lambda}

Visible range: $400$ nm (violet) to $700$ nm (red)

All EM waves are transverse, can travel through vacuum, and are produced by accelerating charges.

Question

Solution — Step by Step

Why This Works

Alternative Method

Common Mistake

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