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: \(\sin 60^\circ = 0.866\))
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: \(\sin 60^\circ = 0.866\))
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Bragg’s law \(n\lambda = 2d\sin\theta\) is used to determine interplanar spacing in crystal lattices.
Updated On: Jun 19, 2026
- 5.2 \AA
- 2.6 \AA
- 3.2 \AA
- 9.0 \AA
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The Correct Option is A
Solution and Explanation
Step 1: Applying Bragg’s law.
The condition for diffraction in crystals is given by Bragg’s equation: \[ n\lambda = 2d \sin\theta \] where \(n\) is order of diffraction, \(\lambda\) is wavelength, \(d\) is interplanar spacing, and \(\theta\) is diffraction angle.
Step 2: Substituting given values.
Here, \(n = 1\), \(\lambda = 9 \,\AA\), and \(\sin 60^\circ = 0.866\). Substituting: \[ 1 \times 9 = 2d \times 0.866 \]
Step 3: Simplifying equation.
\[ 9 = 1.732d \]
Step 4: Solving for \(d\).
\[ d = \frac{9}{1.732} \approx 5.2 \,\AA \]
Step 5: Final interpretation.
Thus, the spacing between crystal planes is approximately \(5.2 \,\AA\), consistent with Bragg diffraction conditions.
Final Answer: \[ \boxed{5.2 \,\AA} \]
The condition for diffraction in crystals is given by Bragg’s equation: \[ n\lambda = 2d \sin\theta \] where \(n\) is order of diffraction, \(\lambda\) is wavelength, \(d\) is interplanar spacing, and \(\theta\) is diffraction angle.
Step 2: Substituting given values.
Here, \(n = 1\), \(\lambda = 9 \,\AA\), and \(\sin 60^\circ = 0.866\). Substituting: \[ 1 \times 9 = 2d \times 0.866 \]
Step 3: Simplifying equation.
\[ 9 = 1.732d \]
Step 4: Solving for \(d\).
\[ d = \frac{9}{1.732} \approx 5.2 \,\AA \]
Step 5: Final interpretation.
Thus, the spacing between crystal planes is approximately \(5.2 \,\AA\), consistent with Bragg diffraction conditions.
Final Answer: \[ \boxed{5.2 \,\AA} \]
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