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: Bragg condition.
\[ n\lambda = 2d\sin\theta \]

Step 2: Smallest spacing.
The smallest spacing that still diffracts comes from the largest possible angle, where $\sin\theta = 1$.

Step 3: Solve for $d$.
\[ d = \frac{1 \times 1.54}{2 \times 1} = 0.77 \]

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