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Chapter 12: Problem 119

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 are comparable to the distance between atomic planes in the crystal lattice, allowing for effective diffraction according to Bragg's law. In contrast, visible light has wavelengths much larger than the atomic distances in crystals, leading to ineffective diffraction and an inability to measure atomic distances.

Step by step solution

01

Introduction to the diffraction phenomenon

Diffraction is a phenomenon that occurs when waves, such as light, encounter an obstacle or an opening, causing the waves to bend around the obstacle or spread out after passing through the opening. The extent of the diffraction depends on the size of the obstacle or opening and the wavelength of the incident wave. In the case of crystals, the atoms are arranged in a regular repeating pattern, known as the crystal lattice, which acts as a "diffraction grating" for the incident waves.
02

The Bragg's law relation to diffraction in crystals

Bragg's law is an equation that describes the relationship between the angles of the incident and diffracted waves, the wavelength of the waves, and the distance between the atomic planes in a crystal lattice. The law states that constructive interference, which is when the waves add up to create a strong signal, occurs if: \( n λ = 2 d \sin{\theta} \) where \( n \) is an integer (the order of diffraction), \( λ \) is the wavelength of the incident wave, \( d \) is the distance between atomic planes, and \( \theta \) is the angle between the incident wave and the atomic plane.
03

Comparison of X-rays and visible light wavelengths

The key difference between X-rays and visible light is their wavelengths. Visible light has wavelengths ranging from approximately 400 to 700 nanometers (nm), while X-rays have much shorter wavelengths, typically between 0.01 and 10 nanometers.
04

Understanding of atomic distances in crystals

The atomic distances in crystals, or the distances between the planes of atoms, are typically on the order of angstroms (\(1 \,Å = 10^{-10} \, m\)). This means that the atomic distances are much smaller than the wavelengths of visible light but are comparable to the wavelengths of X-rays.
05

Conclusion on why X-rays are suitable for measuring atomic distances

According to Bragg's law, constructive interference and, consequently, effective diffraction can only occur when the wavelength of the light source is comparable to the atomic distances in the crystal lattice. Due to their shorter wavelengths, X-rays can effectively diffract through the crystal lattice, allowing scientists to obtain information about the atomic structure of the crystal. In contrast, visible light has wavelengths that are much larger than the atomic distances in crystals. As a result, it is not possible to obtain any useful diffraction pattern using visible light, hence it cannot be used to measure atomic distances in crystals.

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Most popular questions from this chapter

Which of the three-dimensional primitive lattices has a unit cell where none of the internal angles is \(90^{\circ}\) ? (a) Orthorhombic, (b) hexagonal, (c) rhombohedral, (d) triclinic, (e) both rhombohedral and triclinic.

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Aluminum metal crystallizes in a face-centered cubic unit cell. (a) How many aluminum atoms are in a unit cell? (b) What is the coordination number of each aluminum atom? (c) Estimate the length of the unit cell edge, \(a\) , from the atomic radius of aluminum \((1.43 \hat{\mathrm{A}}) .\) (d) Calculate the density of aluminum metal.
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