Discussion
For first-order diffraction, the smallest value of dhkl that can be detected with X-ray having a wavelength of 1.54 Å is _____ Å.
Answer: B
The smallest detectable spacing is 0.77 Å.
Bragg's law for first-order diffraction is \(\lambda = 2d\sin\theta\). Since \(\sin\theta\) cannot exceed 1, a reflection exists only when \(d \ge \lambda/2\):
\[ \begin{aligned} d_{min} &= \frac{\lambda}{2} \\ &= \frac{1.54\ \text{Å}}{2} = 0.77\ \text{Å} \end{aligned} \]
A spacing of 0.38 Å is about \(\lambda/4\); it would need \(\sin\theta = 2\), so no first-order reflection is possible. Spacings of 1.02 and 2.05 Å do diffract, at smaller angles, but they are not the smallest value that can be detected.
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