Question:
Find the interplanar spacing $d_{hkl}$ (in Å) using Bragg’s law.
Given: $n = 1$, $\lambda = 1.54\,\text{Å}$
Use Bragg’s law: $n\lambda = 2d\sin\theta$.
Find the interplanar spacing $d_{hkl}$ (in Å) using Bragg’s law.
Given: $n = 1$, $\lambda = 1.54\,\text{Å}$
Use Bragg’s law: $n\lambda = 2d\sin\theta$.
Given: $n = 1$, $\lambda = 1.54\,\text{Å}$
Use Bragg’s law: $n\lambda = 2d\sin\theta$.
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In X-ray diffraction problems, always remember Bragg’s law:
$n\lambda = 2d\sin\theta$.
If first order reflection is given ($n=1$), the formula simplifies significantly.
Updated On: Feb 15, 2026
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Solution and Explanation
Step 1: Write Bragg’s Law.
Bragg’s law is given by:
\[ n\lambda = 2d\sin\theta. \]
We are given:
\[ n = 1, \lambda = 1.54\,\text{Å}. \]
Step 2: Rearrange for $d$.
\[ d = \frac{n\lambda}{2\sin\theta}. \]
Substituting $n=1$:
\[ d = \frac{1.54}{2\sin\theta}. \]
Step 3: Final Expression.
Thus, interplanar spacing is:
\[ \boxed{ d = \frac{1.54}{2\sin\theta}\;\text{Å} }. \]
(If } $\theta$ \textbf{ is given, substitute directly to compute numerical value.)
Bragg’s law is given by:
\[ n\lambda = 2d\sin\theta. \]
We are given:
\[ n = 1, \lambda = 1.54\,\text{Å}. \]
Step 2: Rearrange for $d$.
\[ d = \frac{n\lambda}{2\sin\theta}. \]
Substituting $n=1$:
\[ d = \frac{1.54}{2\sin\theta}. \]
Step 3: Final Expression.
Thus, interplanar spacing is:
\[ \boxed{ d = \frac{1.54}{2\sin\theta}\;\text{Å} }. \]
(If } $\theta$ \textbf{ is given, substitute directly to compute numerical value.)
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