**Correct Option: B. have extremely short wavelength** ### Detailed Explanation: X-rays are a form of electromagnetic radiation, similar to visible light but with much shorter wavelengths. The wavelength of X-rays typically ranges from about 0.01 to 10 nanometers (nm), which is significantly shorter than that of visible light (approximately 400 to 700 nm). This short wavelength is crucial for studying crystal structures for several reasons: 1. **Size Comparison**: The atomic spacing in crystals is on the order of angstroms (1 angstrom = 0.1 nm). Since X-rays have wavelengths comparable to the distances between atoms in a crystal, they can effectively interact with the crystal lattice. This interaction is essential for techniques like X-ray diffraction, which is used to determine the arrangement of atoms within a crystal. 2. **Diffraction**: When X-rays are directed at a crystal, they are scattered by the electrons surrounding the atoms. The short wavelength allows for constructive and destructive interference patterns to form, which can be analyzed to reveal the crystal structure. The Bragg's Law equation, \( n\lambda = 2d\sin(\theta) \), where \( n \) is an integer, \( \lambda \) is the wavelength of the X-rays, \( d \) is the distance between crystal planes, and \( \theta \) is the angle of incidence, illustrates how the wavelength relates to the crystal structure. 3. **Resolution**: The shorter the wavelength, the higher the resolution of the imaging or diffraction technique. This means that X-rays can provide detailed information about the positions of atoms in a crystal, which is vital for understanding material properties and behaviors. ### Why Other Options Are Incorrect: - **Option A: have a very long-reaching wavelength** This option is incorrect because "long-reaching" implies a longer wavelength, which is not suitable for studying crystal structures. Longer wavelengths (like those of radio waves) are not capable of resolving the fine details of atomic arrangements in crystals. - **Option C: are invisible** While it is true that X-rays are invisible to the human eye, this characteristic does not directly relate to their utility in studying crystal structures. Many forms of radiation, including visible light, can be used for various applications, but the key factor for X-rays is their short wavelength, not their invisibility. - **Option D: are very fast** The speed of X-rays in a vacuum is the same as that of all electromagnetic radiation, which is the speed of light (approximately \( 3 \times 10^8 \) meters per second). While this speed is significant in many contexts, it does not contribute to their effectiveness in studying crystal structures. The critical factor is the wavelength, not the speed. ### Summary of Key Points: - X-rays have extremely short wavelengths (0.01 to 10 nm), comparable to atomic distances. - Their short wavelength allows for effective diffraction and resolution of crystal structures. - Techniques like X-ray diffraction utilize the interaction of X-rays with crystal lattices to reveal atomic arrangements. - Other options (long wavelength, invisibility, speed) do not address the fundamental reason X-rays are used in crystallography. This understanding of X-rays and their properties is essential for students preparing for exams in physics, particularly in topics related to materials science and crystallography.