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Chapter 4: Problem 13

Crystal lattices can be examined with X-rays but not UV. Why?

Short Answer

Expert verified
X-rays are used for analyzing crystal lattices because their wavelengths are comparable to the interatomic distances in crystals, allowing for scattering and constructive interference of incident waves according to Bragg's Law (\(n \lambda = 2 d \sin \theta\)). On the other hand, the larger wavelengths of ultraviolet radiation make them unable to resolve the small distances between atomic planes in a crystal lattice, making X-rays more suitable for studying crystal lattices than ultraviolet radiation.

Step by step solution

01

Understanding crystal lattices

Crystal lattices are a periodic arrangement of atoms, ions, or molecules in a three-dimensional space. These structures have a specific size and shape, which are characterized by the lattice parameters and interatomic distances.
02

Interaction of electromagnetic waves with crystal lattices

When electromagnetic waves, such as X-rays or ultraviolet radiation, are incident on a crystal lattice, they interact with the electron cloud around the atoms. This interaction can result in scattering of the incident waves. The Bragg's Law describes the condition for constructive interference of the scattered waves, which is given by: \[ n \lambda = 2 d \sin \theta \] where \(n\) is an integer, \(\lambda\) is the wavelength of the incident radiation, \(d\) is the distance between the atomic planes in the crystal lattice, and \(\theta\) is the angle of incidence.
03

Comparing X-rays and ultraviolet radiation

X-rays and ultraviolet radiation have different wavelengths. X-rays have a wavelength of about 0.1 - 100 Å (10^(-10) - 10^(-8) meters), while ultraviolet radiation has a wavelength of about 10 - 400 nm (10^(-8) - 10^(-7) meters). The wavelengths of X-rays are much smaller, which allows them to penetrate deeper into the crystal lattice and resolve smaller distances between atomic planes.
04

Reason for using X-rays instead of ultraviolet radiation

X-rays are used for the analysis of crystal lattices because their wavelengths are comparable to the interatomic distances in crystals, which allows for the scattering and constructive interference of the incident waves as described by Bragg's Law. In contrast, the wavelengths of ultraviolet radiation are much larger, making them unable to resolve the small distances between atomic planes in a crystal lattice. Therefore, X-rays are suitable for studying crystal lattices, while ultraviolet radiation is not.

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Most popular questions from this chapter

The analysis shown below also applies to diffraction gratings with lines separated by a distance \(d .\) What is the distance between fringes produced by a diffraction grating having 125 lines per centimeter for 600 -nm light, if the screen is \(1.50 \mathrm{m}\) away? (Hint: The distance between adjacent fringes is \(\Delta y=x \lambda / d, \quad\) assuming the slit separation \(d\) is comparable to \(\lambda_{-}\) )

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