Choose the correct option relating wavelengths of different parts of electromagnetic wave spectrum
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Q: Why do radio waves have the longest wavelength?

Radio waves have the lowest frequency and lowest energy in the EM spectrum. Since wavelength is inversely proportional to frequency ($c = \nu \lambda$), they naturally have the longest wavelengths.

Q: How can I easily remember the order of the EM spectrum?

A common mnemonic is 'Roman Men Invented Very Unusual X-ray Guns' which stands for Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma ray. This is in order of increasing frequency and decreasing wavelength.

Q: Are microwaves shorter than radio waves?

Yes, microwaves have shorter wavelengths and higher frequencies than radio waves. They are often considered a sub-category of radio waves but are distinct in their applications like cooking and radar.

Q: What is the wavelength range of visible light?

Visible light ranges approximately from $380 \text{ nm}$ (violet) to $700 \text{ nm}$ (red), which is equivalent to $3800 \text{ \AA}$ to $7000 \text{ \AA}$.

Q: Why are X-rays dangerous but radio waves are not?

X-rays have very short wavelengths and high energy, making them ionizing radiation capable of damaging living tissue. Radio waves have long wavelengths and low energy, making them non-ionizing and generally safe.

Question

Choose the correct option relating wavelengths of different parts of electromagnetic wave spectrum Options: (A) $\lambda_{X-rays} < \lambda_{microwaves} < \lambda_{radio waves} < \lambda_{visible}$ (B) $\lambda_{visible} > \lambda_{X-rays} > \lambda_{radio waves} > \lambda_{microwaves}$ (C) $\lambda_{radio waves} > \lambda_{microwaves} > \lambda_{visible} > \lambda_{X-rays}$ (D) $\lambda_{visible} < \lambda_{microwaves} < \lambda_{radio waves} < \lambda_{X-rays}$

Sigma Percentile · Accepted Answer

### The Electromagnetic Spectrum: A Journey of Wavelengths

The electromagnetic spectrum is a fascinating continuum of waves that permeate our universe. From the high-energy gamma rays emitted by radioactive decay to the long radio waves that carry our favorite songs, the spectrum is incredibly diverse. In this problem, we are tasked with arranging four specific types of electromagnetic waves—X-rays, visible light, microwaves, and radio waves—in order of their wavelengths.

### Understanding the Relationship Between Energy and Wavelength

Before we dive into the specific values, it is crucial to remember the fundamental relationship between the energy of an electromagnetic wave and its wavelength. According to Planck's equation, the energy $E$ of a photon is given by:

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

where $h$ is Planck's constant, $c$ is the speed of light, and $\lambda$ is the wavelength. This equation tells us that energy and wavelength are **inversely proportional**. Waves with the highest energy have the shortest wavelengths, and waves with the lowest energy have the longest wavelengths.

### Analyzing the Given Waves

Let's break down the four types of waves mentioned in the question, starting from the most energetic:

**1. X-rays:**
X-rays are highly energetic waves capable of penetrating soft tissue, which is why they are so useful in medical imaging. Because of their high energy, they have very short wavelengths. Typically, the wavelength of X-rays ranges from about $0.01 	ext{ \AA}$ to $100 	ext{ \AA}$.

**2. Visible Light:**
This is the narrow band of the electromagnetic spectrum that our eyes have evolved to detect. It sits roughly in the middle of the spectrum. The wavelength of visible light ranges from approximately $3800 	ext{ \AA}$ (violet) to $7000 	ext{ \AA}$ (red).

**3. Microwaves:**
Moving further down the energy scale, we encounter microwaves. These waves are commonly used in radar technology and, of course, microwave ovens. Their wavelengths are significantly longer than visible light, ranging from about $10^7 	ext{ \AA}$ to $3 	imes 10^9 	ext{ \AA}$.

**4. Radio Waves:**
Finally, we reach radio waves. These waves have the lowest energy and, consequently, the longest wavelengths in the entire electromagnetic spectrum. They are used extensively in communication systems. The wavelength of radio waves starts from around $10^9 	ext{ \AA}$ and can extend to $10^{15} 	ext{ \AA}$ and beyond.

### The Final Verdict

By comparing these ranges, the order becomes crystal clear. Radio waves stretch out the longest, followed by microwaves, then the visible light we see every day, and finally, the tightly packed X-rays.

Mathematically, we can express this relationship as:

$$\lambda_{	ext{radio waves}} > \lambda_{	ext{microwaves}} > \lambda_{	ext{visible}} > \lambda_{	ext{X-rays}}$$

This perfectly matches option (c). Remembering the order of the electromagnetic spectrum is a fundamental skill in physics, and understanding the inverse relationship between energy and wavelength makes recalling this order a breeze!

Animated Solution for Physics - Electromagnetic Waves: Choose the correct option relating wavelengths of different parts of electromagnetic wave spectrum

Select Answer:

Visualized Solution

$The Electromagnetic Spectrum$

$Wavelength of X-rays$

$Wavelength of Visible Light$

$Wavelength of Microwaves$

$Wavelength of Radio Waves$

$Final Comparison$

The Sigma Insight: Characteristics of Electromagnetic Waves

The Electromagnetic Spectrum

Understanding the Relationship Between Energy and Wavelength

Analyzing the Given Waves

The Final Verdict

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