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Difficulty: MediumX-rays: Production, Properties, and Applications

X-rays undergo diffraction when passed through crystalline solids because the interplanar atomic spacing of a crystal lattice is comparable to the wavelength of X-rays.

Answer: Answer

Answer

The statement is true. X-rays have wavelengths of approximately 10−10 m10^{-10}\text{ m}, which is of the same order of magnitude as the spacing between adjacent atomic planes in crystal lattices, allowing crystals to act as natural diffraction gratings.
The statement is true because wave diffraction requires the grating aperture or obstacle spacing to be of the same order of magnitude as the incident wavelength. Since X-ray wavelengths (approx. 10−10 m10^{-10}\text{ m}) match the interatomic spacing of crystals, crystalline solids act as effective diffraction gratings.

Step-by-Step Solution

1
Identify the characteristic wavelength range of X-rays.
X-rays are high-energy electromagnetic waves with wavelengths typically ranging from 10−11 m10^{-11}\text{ m} to 10−8 m10^{-8}\text{ m} (around 0.1 nm0.1\text{ nm}).
Wave diffraction requires the width of the aperture or obstacle spacing to be comparable in size to the wavelength of the incident wave.
2
Determine the interatomic spacing of crystalline solids.
The distance between neighboring atomic planes in a typical crystal lattice is on the order of 10−10 m10^{-10}\text{ m} (0.1 nm0.1\text{ nm} to 0.3 nm0.3\text{ nm}).
Comparing these dimensions shows that crystal lattice spacing matches X-ray wavelengths.
3
Evaluate the condition for wave diffraction.
Because the interatomic spacing matches the X-ray wavelength, constructive and destructive interference occurs, forming diffraction patterns.
This confirms that the given statement is true.

Key Concept

X-ray Diffraction by Crystal Lattices
Estimated Time:1m 0s
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Topics

X-rays: Production, Properties, and Applications

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