Question

The Bragg condition is given by:

• A. \(\vec{K}\cdot\vec{G}+G=0\)
• B. \(\vec{K}\cdot\vec{G}+G^2=0\)
• C. \(2\vec{K}\cdot\vec{G}+G=0\)
• D. \(2\vec{K}\cdot\vec{G}+G^2=0\)

Hint:

In reciprocal space, Bragg condition can be written as \(2\vec{K}\cdot\vec{G}+G^2=0\).

Answer 1

The Correct Option is D

Concept:
In reciprocal lattice notation, Bragg diffraction occurs when the change in wave vector is equal to a reciprocal lattice vector.

Step 1: Write diffraction condition.
For elastic scattering: \[ |\vec{K}+\vec{G}|^2=|\vec{K}|^2 \]

Step 2: Expand the left side. \[ (\vec{K}+\vec{G})\cdot(\vec{K}+\vec{G})=\vec{K}\cdot\vec{K} \] \[ K^2+2\vec{K}\cdot\vec{G}+G^2=K^2 \]

Step 3: Simplify. \[ 2\vec{K}\cdot\vec{G}+G^2=0 \] \[ \therefore \text{Correct Answer is (D)} \]