Question

If the angle of diffraction (\(\theta\)) is \(60^\circ\) for 9 \AA wavelength of x-rays, what is the spacing between two planes of a solid substance for a first order diffraction (\(n=1\))? (Given: \(\sin 60^\circ = 0.866\))

• A. 5.2 \AA
• B. 2.6 \AA
• C. 3.2 \AA
• D. 9.0 \AA

Hint:

Bragg’s law \(n\lambda = 2d\sin\theta\) is used to determine interplanar spacing in crystal lattices.

Answer 1

The Correct Option is A

Step 1: Recalling Bragg's condition.
Constructive interference occurs when nλ = 2d sinθ, with n = order, λ = wavelength, d = interplanar spacing, θ = diffraction angle.

Step 2: Inserting the provided data.
For first-order diffraction (n=1), λ = 9 Å, and sin60° = 0.866: 1×9 = 2d × 0.866.

Step 3: Simplifying the equation.
9 = 1.732 d.

Step 4: Solving for d.
d = 9/1.732 ≈ 5.2 Å.

Step 5: Interpretation.
The crystal plane separation is roughly 5.2 Å, fulfilling the diffraction requirement.