Step 1: Understanding the Topic
This question involves Bragg's Law, a fundamental principle in X-ray crystallography. The law describes the condition for constructive interference of X-rays scattered by the parallel planes of atoms in a crystal. This allows us to determine the interplanar spacing ($d$) if the X-ray wavelength ($\lambda$) and the diffraction angle ($\theta$) are known.
Step 2: Key Formula - Bragg's Law
The equation for Bragg's Law is:
\[
n\lambda = 2d\sin\theta
\]
where:
$n$ is an integer representing the order of the reflection (given as 1 for first-order).
$\lambda$ is the wavelength of the X-rays (given as 1.54 Å).
$d$ is the spacing between the crystal planes (the value we need to find).
$\theta$ is the angle of incidence (Bragg angle) of the X-rays.
Step 3: Detailed Calculation
We are asked to find an expression for the interplanar spacing, $d$. To do this, we need to rearrange Bragg's Law to solve for $d$:
\[
d = \frac{n\lambda}{2\sin\theta}
\]
Now, we substitute the given values into this rearranged equation:
$n = 1$
$\lambda = 1.54\,\text{Å}$
\[
d = \frac{(1)(1.54\,\text{Å})}{2\sin\theta}
\]
\[
d = \frac{1.54}{2\sin\theta}\,\text{Å}
\]
This expression gives the interplanar spacing in terms of the diffraction angle $\theta$.
Step 4: Final Answer
The final expression for the interplanar spacing is:
\[
\boxed{
d = \frac{1.54}{2\sin\theta}\;\text{Å}
}
\]
To get a numerical value, a specific angle $\theta$ for the diffraction peak would need to be provided.