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: $n\lambda = 2d\sin\theta$.

Hint:

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.

Answer 1

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.)