Question

In Bragg's equation for diffraction of X-rays, \(n\) represents a) number of moles b) quantum number c) order of reflection d) Avogadro number

Short answer

In Bragg's Equation, \(n\) represents the 'order of reflection'. So, the correct option is 'c) order of reflection'.

Step-by-step solution

Understanding Bragg's Equation

Bragg's Law or equation is given as \(n\lambda = 2d\sin\theta\), where: - \(\lambda\): is the wavelength of incident wave, - \(d\): is the distance between the planes in the atomic lattice, - \(\theta\): is the angle of incidence.This equation is used to determine the angles for coherent and incoherent scattering from a crystal lattice.

Understanding the Role of 'n' in Bragg's Equation

In Bragg's equation, \(n\) is an integer and it denotes the order of reflection or scatter. It represents the fact that reflections can occur not just from the first layer of atoms, but from deeper layers as well.

Matching the Option

Based on the understanding from Step 2, it becomes apparent that in Bragg's equation, \(n\) represents the 'order of reflection'. Hence, option 'c) order of reflection' is the correct answer.

Key concepts

X-ray diffraction

X-ray diffraction is a scientific method used to study the structure of crystals. When X-rays are directed at a crystal, they are scattered in different directions. This scattering happens because of the interaction between the X-rays and the atoms within the crystal, which are arranged in a regular pattern. The pattern formed by the scattered X-rays is like a fingerprint of the structure inside the crystal.

A key aspect that makes X-ray diffraction so powerful is its ability to precisely determine the arrangement of atoms. By analyzing the directions and the intensity of the scattered X-rays, scientists can understand the exact positions of atoms in the crystal. This is crucial in fields such as materials science and chemistry, where knowing the atomic structure is essential for understanding material properties.

• X-rays are high-energy electromagnetic waves.
• They can penetrate solids, making them ideal for examining internal structures.

order of reflection

In the context of Bragg’s Law, the term 'order of reflection' refers to the integer 'n' in the equation. Bragg’s Law is expressed as \( n\lambda = 2d\sin\theta \), where \( n \) indicates the order of reflection. It tells us how many wavelengths fit into the path difference between the waves reflecting from different planes in the crystal.

When the X-rays reflect off the layers of a crystal, they can do so from different levels or planes within the crystal structure. The order of reflection represents these different levels. The first order of reflection \( (n = 1) \) refers to the immediate next plane, the second order \( (n = 2) \) to the one after that, and so on.

• The order of reflection can help understand deeper structural layers.
• Multiple orders lead to more accurate and detailed information about the crystal.

crystal lattice

A crystal lattice is a highly ordered arrangement of atoms or molecules repeated in all three spatial dimensions. Imagine it as a three-dimensional grid or pattern made up of tiny points, where each point represents an atom or a molecule.

This ordered arrangement gives rise to various unique properties of crystals, such as symmetry and ability to diffract X-rays. The distance between these repeating points, known as lattice spacing or interplanar distance, plays a crucial role in diffraction experiments like X-ray diffraction.

• The orderly structure leads to predictable properties.
• Lattice spacing is a key factor in Bragg's Law.

interference pattern

An interference pattern arises when two sets of waves overlap. In the context of X-ray diffraction, this occurs when X-rays reflect off the different layers within a crystal.

As waves reflect from different planes, they can either reinforce or cancel each other depending on the paths they take relative to each other. Constructive interference happens when the waves strengthen each other, leading to detectable peaks in intensity. Destructive interference occurs when waves cancel out, leading to minima in the pattern.

• Constructive interference results in higher intensity.
• Destructive interference causes lower intensity areas.