Understanding Bragg's Law

Bragg's law is a fundamental principle in X-ray crystallography concerning the diffraction of X-rays by crystal lattices. When X-rays interact with the atoms in a crystal, they are scattered. Constructive interference occurs only when the path difference between waves scattered by successive atomic planes is an integer multiple of the wavelength.

This condition for constructive interference is described by Bragg's law.

The Bragg's Law Equation

Bragg's law is mathematically expressed as:

$$n\lambda = 2d \sin\theta$$

Let's break down the components of this equation:

• n: An integer representing the order of diffraction (e.g., 1, 2, 3, ...). This corresponds to the order of the bright spot observed in the diffraction pattern.
• λ (lambda): The wavelength of the incident X-ray beam.
• d: The distance between adjacent parallel atomic planes in the crystal lattice.
• θ (theta): The angle of incidence of the X-ray beam on the crystal plane (also the angle of reflection).

The equation essentially relates the geometry of the crystal lattice (d) and the angle of incidence (θ) to the wavelength of the X-rays (λ) and the order of the diffraction peak (n).

Analyzing the Given Equations for Bragg's Law

We are asked to identify the equation that represents Bragg's law from the given options. Let's compare each option with the standard Bragg's law equation, $n\lambda = 2d \sin\theta$.

• Option 1: $n\lambda = 2\sin\theta$
  This equation is missing the interplanar distance term 'd'. Therefore, it does not represent Bragg's law.
• Option 2: $n\lambda = 2d \sin\theta$
  This equation exactly matches the standard mathematical expression for Bragg's law, where n is the order of diffraction, λ is the wavelength, d is the interplanar distance, and θ is the angle of incidence.
• Option 3: $2n\lambda = 2d \sin\theta$
  This equation has $2n\lambda$ on the left side instead of $n\lambda$. This form is not the correct representation of Bragg's law.

Based on the comparison, only Option 2 correctly represents Bragg's law.