Arrange the following in the ascending order of wavelength:
(A) Gamma rays (\( \lambda_1 \))
(B) X-ray (\( \lambda_2 \))
(C) Infrared waves (\( \lambda_3 \))
(D) Microwaves (\( \lambda_4 \))
Choose the most appropriate answer from the options given below:
(A) Gamma rays (\( \lambda_1 \))
(B) X-ray (\( \lambda_2 \))
(C) Infrared waves (\( \lambda_3 \))
(D) Microwaves (\( \lambda_4 \))
Choose the most appropriate answer from the options given below:
- \( \lambda_4<\lambda_3<\lambda_1<\lambda_2 \)
- \( \lambda_4<\lambda_3<\lambda_2<\lambda_1 \)
- \( \lambda_1<\lambda_2<\lambda_3<\lambda_4 \)
- \( \lambda_2<\lambda_1<\lambda_4<\lambda_3 \)
The Correct Option is C
Approach Solution - 1
To determine the order of wavelengths from shortest to longest for the given types of electromagnetic waves, we need to first understand the general spectrum of electromagnetic radiation. The electromagnetic spectrum, ordered from shortest wavelength to longest, is as follows:
- Gamma rays
- X-rays
- Ultraviolet (not part of the question, but included for context)
- Visible light (not part of the question, but included for context)
- Infrared waves
- Microwaves
- Radio waves (not part of the question, but included for context)
Based on this electromagnetic spectrum, we can arrange the given electromagnetic waves in the order of increasing wavelength:
- Gamma rays (\(\lambda_1\))
- X-rays (\(\lambda_2\))
- Infrared waves (\(\lambda_3\))
- Microwaves (\(\lambda_4\))
This sequence corresponds to the option: \(\lambda_1<\lambda_2<\lambda_3<\lambda_4\)
Hence, the correct answer is: \(\lambda_1<\lambda_2<\lambda_3<\lambda_4\)
Approach Solution -2
To determine the ascending order of wavelengths for the given types of electromagnetic waves, we need to understand their relative positions in the electromagnetic spectrum. The electromagnetic spectrum is a range of all types of electromagnetic radiation, organized by their wavelengths or frequencies.
- Gamma rays (\(\lambda_1\)): These are at the high-energy end of the spectrum, possessing the shortest wavelengths and highest frequencies.
- X-rays (\(\lambda_2\)): These have slightly longer wavelengths than gamma rays, but are still quite short compared to other types of radiation.
- Infrared waves (\(\lambda_3\)): These have wavelengths longer than those of visible light and are used for thermal imaging.
- Microwaves (\(\lambda_4\)): These have the longest wavelengths among the options given and are used in various applications including cooking and communications.
Based on the above information, we can arrange these in ascending order of their wavelengths:
| Type of Radiation | Order in Spectrum |
|---|---|
| Gamma rays (\(\lambda_1\)) | Shortest wavelength |
| X-rays (\(\lambda_2\)) | Next shortest wavelength |
| Infrared waves (\(\lambda_3\)) | Middle wavelengths |
| Microwaves (\(\lambda_4\)) | Longest wavelength |
The correct ascending order of their wavelengths is: \(\lambda_1<\lambda_2<\lambda_3<\lambda_4\)
Therefore, the correct answer is the third option: \( \lambda_1<\lambda_2<\lambda_3<\lambda_4 \).
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