why we cannot use visible light for studying the crystal structure using Bragg’s diffraction method?

We cannot use visible light for studying crystal structure using Bragg's diffraction method because the wavelength of visible light is relatively large compared to the spacing of atoms in a crystal lattice. To understand why this is a problem, let's first explain the basic principle of Bragg's diffraction.

Bragg's diffraction is a technique used to investigate the arrangement of atoms or molecules within a crystal lattice. It is based on the phenomenon of constructive interference of waves. When a beam of X-rays (or other similarly short wavelength radiation) is incident on a crystal, the X-rays interact with the atoms in the crystal and undergo diffraction, resulting in a pattern of spots or lines on a detector.

The key requirement for the diffraction to occur is that the wavelength of the incident radiation should be similar to the spacing of the atoms in the crystal lattice. According to Bragg's law, the condition for constructive interference is given by 2d sinθ = nλ, where d is the spacing between the crystal planes, θ is the angle of incidence, n is an integer, and λ is the wavelength of the incident radiation.

The problem with using visible light for studying crystal structures is that its wavelength is typically in the range of a few hundred nanometers (nm) to several hundred nanometers, which is much larger than the atomic spacing in a crystal lattice. The spacing between atoms in a crystal lattice is usually on the order of angstroms (Å), which is one-tenth of a nanometer. As a result, the visible light does not satisfy the condition of Bragg's law and cannot produce a detectable diffraction pattern.

To overcome this limitation, shorter wavelength radiation such as X-rays or high-energy electrons are used in Bragg's diffraction experiments. X-rays have wavelengths in the range of 0.1 to 10 angstroms, which are comparable to the atomic spacing in crystals. This allows for the diffraction of X-rays by the crystal lattice, enabling the determination of the crystal structure based on the resulting diffraction pattern.

In summary, we cannot use visible light for studying crystal structure using Bragg's diffraction method because its wavelength is much larger than the spacing between the atoms in a crystal lattice. The technique requires radiation with wavelengths similar to the atomic spacing, such as X-rays, to produce a detectable diffraction pattern.