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Chapter 19: Problem 133

Which of the following radiations has the least wavelength? (A) \(\gamma\)-rays (B) \(\beta\)-rays (C) \(\alpha\)-rays (D) \(X\)-rays

Short Answer

Expert verified
The answer is (A) \(\gamma\)-rays. Gamma rays have the least wavelength among the given types of radiations, with typical wavelengths of less than \[10^{-12}\] m.

Step by step solution

01

Recall the Electromagnetic Spectrum

First, let's recall the electromagnetic spectrum from the highest energy to the lowest energy (shortest wavelength to longest wavelength): 1. Gamma Rays (\(\gamma\)-rays) 2. X-rays 3. Ultraviolet Rays 4. Visible Light 5. Infrared 6. Microwaves 7. Radio Waves Beta (\(\beta\)-rays) and alpha (\(\alpha\)-rays) are not a part of the electromagnetic spectrum, but we will consider their typical wavelengths as well.
02

Typical Wavelengths of Radiations

Let's look at the given options and their typical wavelengths: (A) \(\gamma\)-rays: Shortest wavelength of less than \[10^{-12}\] m and highest energy. (B) \(\beta\)-rays: Wavelength depends upon the energy of the individual electron, but typically much longer than gamma rays, in the range of \[10^{-12}\] m to \[10^{-9}\] m. (C) \(\alpha\)-rays: Wavelengths of around \[10^{-11}\] m to \[10^{-9}\] m for alpha particles. (D) \(X\)-rays: Wavelengths lie in the range of \[10^{-12}\] m to \[10^{-9}\] m, having energy lower than gamma rays but higher than other radiations in the list.
03

Comparing the Wavelengths

Comparing the wavelengths of the given options, we see that gamma rays have the shortest wavelength of less than \[10^{-12}\] m. Therefore:
04

Conclusion

The answer is (A) \(\gamma\)-rays. Gamma rays have the least wavelength among the given types of radiations.

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