Question

For first-order diffraction, the smallest value of $d_{hkl}$ that can be detected with X-ray having a wavelength of 1.54 is _ _ _ .

• A. 0.38
• B. 0.77
• C. 1.02
• D. 2.05

Hint:

For minimum $d$, always take $\sin\theta = 1$ in Bragg’s lawThis gives the resolution limit of X-ray diffraction

Answer 1

The Correct Option is B

Step 1: Use Bragg's Law.
\[ n\lambda = 2d\sin\theta \]
For first-order diffraction: $n = 1$

Step 2: Condition for smallest $d$.
The smallest interplanar spacing $d$ is obtained when $\sin\theta = 1$ (i.e., $\theta = 90^\circ$)

Step 3: Substitute values.
\[ d = \frac{n\lambda}{2\sin\theta} = \frac{1 \times 1.54}{2 \times 1} \]
\[ d = \frac{1.54}{2} = 0.77 \, \text{\AA} \]

Step 4: Conclusion.
\[ \boxed{0.77 \, \text{\AA}} \]