In Bragg's law, the concept of "integer multiple of wavelength" refers to the constructive interference of waves that occurs when the path length traveled by the waves differs by a whole number of wavelengths.
Bragg's law is used to explain the diffraction of X-rays or other waves by a crystal lattice. When a wave interacts with a crystal lattice, it can be scattered by the atoms within the lattice. The scattered waves interfere with each other, leading to constructive and destructive interference patterns.
According to Bragg's law, the condition for constructive interference in a crystal lattice occurs when the path length difference between two waves scattered from adjacent planes of atoms is equal to an integer multiple of the wavelength of the incident wave.
Mathematically, Bragg's law can be expressed as:
2d sin(theta) = nλ
Where:
- d is the spacing between adjacent crystal planes.
- theta is the angle of incidence of the incident wave with respect to the crystal lattice.
- n is an integer representing the order of the diffraction peak.
- lambda (λ) is the wavelength of the incident wave.
The equation states that when the path length difference between the waves is equal to n times the wavelength, constructive interference occurs. This results in a strong diffraction peak for that particular angle of incidence and order of diffraction.
In simpler terms, if the path length difference between the waves scattered from adjacent planes of atoms is a whole number of wavelengths, the waves will add up constructively, reinforcing each other and producing a strong diffraction signal. This occurs at specific angles of incidence and is observed as bright spots or diffraction peaks in the X-ray or wave pattern.
By analyzing the angles at which these diffraction peaks occur, scientists can obtain valuable information about the arrangement of atoms within the crystal lattice, such as the interatomic spacing and the crystal structure.