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Chapter 12: Problem 105

Explain why X-rays can be used to measure atomic distances in crystals but visible light cannot be used for this purpose.

Short Answer

Expert verified
X-rays can be used to measure atomic distances in crystals because their wavelengths (approximately \(0.01\,\text{nm}\) to \(10\,\text{nm}\)) are on the same order of magnitude as the atomic distances (approximately \(0.1\,\text{nm}\) to \(1\,\text{nm}\)) in crystal lattices. This enables X-rays to interact with the crystal lattice via diffraction. Conversely, visible light's wavelengths (approximately \(380\,\text{nm}\) to \(750\,\text{nm}\)) are much larger than atomic distances, making it unable to diffract off the lattice planes and thus unable to measure atomic distances in crystals.

Step by step solution

01

Explain the phenomena to be compared

X-rays and visible light are both part of the electromagnetic spectrum, with X-rays having much shorter wavelengths than visible light. The wavelengths of X-rays typically fall within the range of approximately 0.01 nm to 10 nm, whereas visible light spans from around 380 nm to 750 nm.
02

Introduce crystal structure and atomic distances

In a crystal lattice, the atoms are arranged in a periodic pattern. The distances between these atoms, known as atomic distances or interatomic distances, typically fall within the range of 0.1 nm to 1 nm. When studying these structures, scientists use a technique called diffraction to determine the atomic distances.
03

Outline the concept of diffraction

Diffraction is a phenomenon whereby a wave, such as an electromagnetic wave, bends around the edges or scatters off an object. In order to observe diffraction, the size of the object or the distance between the points in a structure should be on the same order of magnitude as the wavelength of the wave being used. For X-rays and visible light, this refers to the wavelengths mentioned in Step 1.
04

Compare X-ray wavelengths to atomic distances

As mentioned earlier, X-ray wavelengths typically range from approximately \(0.01\,\text{nm}\) to \(10\,\text{nm}\), which are on the same order of magnitude as atomic distances in crystal lattices (\(0.1\,\text{nm}\) to \(1\,\text{nm}\)). This allows X-rays to diffract off the lattice planes in the crystal, providing information on the distances between atoms.
05

Compare visible light wavelengths to atomic distances

On the other hand, visible light wavelengths fall within the range of approximately \(380\,\text{nm}\) to \(750\,\text{nm}\), which is much larger than the atomic distances in a crystal lattice. This means that visible light is unable to diffract off the lattice planes, and therefore cannot be used to measure atomic distances.
06

Conclusion

In summary, X-rays can be used to measure atomic distances in crystals because their wavelengths are on the same order of magnitude as the atomic distances, allowing them to interact with the crystal lattice via diffraction. Visible light, with its considerably larger wavelengths, is unable to diffract off the lattice planes and therefore cannot provide information on atomic distances in crystals.

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