Match the following (i) X-rays (ii) UV (iii) Long – Class 11 Chemistry

NCERT Exemplar · Q45

Q. Match the following

(i) X-rays

(ii) UV

(iii) Long radio waves

(iv) Microwave

(a) ν = 10^0 - 10^4 Hz

(b) ν = 10^10 Hz

(d) ν = 10^18 Hz

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Concept understanding — Electromagnetic Wave Wavelength

What is Wavelength? The Intuition First

Imagine dropping a pebble into a still pond. Ripples spread outward — evenly spaced circles. The distance between two consecutive crests (the highest points) is what we call wavelength. It's the "repeat length" of the wave.

Now, electromagnetic waves are not water waves. They don't need a medium. But the same idea holds: an EM wave is a travelling disturbance in electric and magnetic fields. As it moves, the fields oscillate — they go up, down, up, down. The wavelength ( $\lambda$ , Greek letter lambda) is the distance over which the wave's shape repeats.

Note

In a vacuum, all EM waves travel at the same speed: $c = 3 \times 10^8 \ \text{m/s}$ . What changes from one wave to another is the wavelength (and its partner, frequency).

The Precise Definition

For a sinusoidal electromagnetic wave travelling in one direction, the electric field at a fixed instant of time looks like a sine curve in space. The wavelength $\lambda$ is the spatial distance between two successive points that are in phase — for example, from one crest to the next crest, or from one trough to the next trough.

Mathematically, if the electric field at position $x$ and time $t$ is given by

E(x,t) = E_0 \sin(kx - \omega t)

then the wave number $k$ is related to wavelength by

k = \frac{2\pi}{\lambda}

So $\lambda$ is the distance needed for the argument $kx$ to change by $2\pi$ — one full cycle of the sine wave.

The Fundamental Relationship

The wavelength, frequency $f$ , and speed $c$ are tied together by a simple equation:

c = f \lambda

This is the wave equation for EM waves in vacuum. It means:

If the wavelength is long, the frequency is low.
If the wavelength is short, the frequency is high.
The product is always $c$ , a constant.

Tip

To remember: think of a marching band. If soldiers take long strides (large $\lambda$ ), they take fewer steps per second (low $f$ ). If they take short, quick steps (small $\lambda$ ), they take many steps per second (high $f$ ). The speed of the band is fixed — stride length × steps per second.

The Electromagnetic Spectrum

Wavelength is what separates different kinds of EM radiation. Here's the spectrum from longest to shortest wavelength:

Type of EM Wave	Approximate Wavelength Range
Radio waves	$> 0.1 \ \text{m}$ (up to km)
Microwaves	$1 \ \text{mm}$ to $0.1 \ \text{m}$
Infrared	$700 \ \text{nm}$ to $1 \ \text{mm}$
Visible light	$400 \ \text{nm}$ to $700 \ \text{nm}$
Ultraviolet	$10 \ \text{nm}$ to $400 \ \text{nm}$
X-rays	$0.01 \ \text{nm}$ to $10 \ \text{nm}$
Gamma rays	$< 0.01 \ \text{nm}$

Watch out

A common mistake: thinking that wavelength is the "size" of the wave. It's not. It's the repeat distance. A radio wave can have a wavelength of 1 km, but its amplitude (the strength of the field) might be tiny. Wavelength and amplitude are independent properties.

Why Wavelength Matters …

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The electromagnetic spectrum is organized by frequency (or wavelength). Matching each region to its characteristic frequency: X-rays → $10^{18}$ Hz, UV → $10^{16}$ Hz, Microwaves → $10^{10}$ Hz, Long radio waves → $10^0 - 10^4$ Hz.

Understanding the Electromagnetic Spectrum

The electromagnetic spectrum spans an enormous range of frequencies, from radio waves that oscillate just a few times per second to gamma rays vibrating trillions of trillions of times per second. Each region has characteristic frequencies that determine its energy and how it interacts with matter.

The key insight is that higher frequency means higher energy (since $E = h\nu$ ), and the spectrum follows a natural ordering from low-energy radio waves through visible light to high-energy X-rays and gamma rays.

c = \nu \lambda

Matching Each Region

Let me work through the spectrum from lowest to highest frequency:

Long radio waves have the lowest frequencies in the electromagnetic spectrum. These are used for AM radio broadcasting, submarine communication, and can have wavelengths of kilometers. Their frequencies range from a few Hz up to about $10^4$ Hz (10 kHz). This matches (a) $\nu = 10^0 - 10^4$ Hz.
Microwaves sit between radio waves and infrared. Used in radar, satellite communication, and microwave ovens, they typically have frequencies around $10^9$ to $10^{11}$ Hz. The given value of $10^{10}$ Hz (10 GHz) is squarely in the microwave range. This matches (b) $\nu = 10^{10}$ Hz.
Ultraviolet (UV) radiation lies just beyond visible light on the high-frequency side. UV from the Sun causes sunburn and is divided into UV-A, UV-B, and UV-C. UV frequencies range from about $10^{15}$ to $10^{17}$ Hz, with $10^{16}$ Hz being characteristic. This matches (c) $\nu = 10^{16}$ Hz. …

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Q.Match the following

Understanding the Electromagnetic Spectrum

Matching Each Region

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