Question

Arrange the following in the ascending order of wavelength (\( \lambda \)): 
(A) Microwaves (\( \lambda_1 \)) 
(B) Ultraviolet rays (\( \lambda_2 \)) 
(C) Infrared rays (\( \lambda_3 \)) 
(D) X-rays (\( \lambda_4 \)) 
Choose the most appropriate answer from the options given below:

• A. \( \lambda_4<\lambda_3<\lambda_1<\lambda_2 \)
• B. \( \lambda_3<\lambda_4<\lambda_1<\lambda_2 \)
• C. \( \lambda_4<\lambda_2<\lambda_3<\lambda_1 \)
• D. \( \lambda_3<\lambda_4<\lambda_2<\lambda_1 \)

Hint:

The electromagnetic spectrum orders radiation based on wavelength. Shorter wavelengths correspond to higher energy and frequency (X-rays, ultraviolet), while longer wavelengths correspond to lower energy (microwaves, infrared).

Answer 1

The Correct Option is A

In the electromagnetic spectrum, the wavelength (\( \lambda \)) of different types of electromagnetic radiation varies as follows:

• \( \lambda_4 \) (X-rays) have the shortest wavelength.
• \( \lambda_3 \) (Infrared rays) have longer wavelengths than X-rays but shorter than microwaves.
• \( \lambda_1 \) (Microwaves) have longer wavelengths than infrared rays but shorter than ultraviolet rays.
• \( \lambda_2 \) (Ultraviolet rays) have the longest wavelength of all.

Thus, the correct order is:

\[ \lambda_4 < \lambda_3 < \lambda_1 < \lambda_2. \]

Final Answer: \( \lambda_4 < \lambda_3 < \lambda_1 < \lambda_2 \).

Answer 2

Step 1: Understand the order of electromagnetic waves.
The electromagnetic spectrum is made up of different types of waves, arranged in increasing order of frequency and decreasing order of wavelength. The general order of different types of waves is:
- Gamma rays have the shortest wavelength, followed by X-rays, ultraviolet rays, visible light, infrared rays, microwaves, and radio waves with the longest wavelength.
Step 2: Wavelength comparison between the given types of waves.
- X-rays (\( \lambda_4 \)) have the shortest wavelength among the given types. X-rays have wavelengths in the range of 0.01 to 10 nanometers.
- Infrared rays (\( \lambda_3 \)) have longer wavelengths than X-rays, typically ranging from 700 nanometers to 1 millimeter.
- Microwaves (\( \lambda_1 \)) have wavelengths ranging from 1 millimeter to 1 meter, which are longer than infrared rays.
- Ultraviolet rays (\( \lambda_2 \)) have shorter wavelengths than visible light but longer wavelengths than X-rays, typically ranging from 10 to 400 nanometers.

Step 3: Conclusion.
The correct order of wavelengths from shortest to longest is: \( \lambda_4 \lt \lambda_3 \lt \lambda_1 \lt \lambda_2 \).

Final Answer:
\[ \boxed{\lambda_4 \lt \lambda_3 \lt \lambda_1 \lt \lambda_2} \]