Question

The diffraction pattern of a crystalline solid gave a peak at \( 2\theta = 60^\circ \). Its ‘d’ value is 1.54 Å. What is the wavelength (in cm) of X-rays used?

• A. \( 1.54 \)
• B. \( 8.89 \times 10^{-9} \)
• C. \( 1.54 \times 10^{8} \)
• D. \( 1.54 \times 10^{-8} \)

Hint:

- Bragg’s equation is fundamental in X-ray diffraction analysis. - The wavelength of X-rays is typically in the order of \( 10^{-8} \) cm. - Convert all units properly before substitution.

Answer 1

The Correct Option is D

Step 1: Use Bragg’s equation Bragg’s law states: \[ n\lambda = 2d \sin\theta \] where, \( n = 1 \) (given), \( d = 1.54 \) Å = \( 1.54 \times 10^{-8} \) cm, \( 2\theta = 60^\circ \Rightarrow \theta = 30^\circ \), \( \sin 30^\circ = 0.5 \). 

Step 2: Compute the wavelength Substituting the values in Bragg’s equation: \[ \lambda = \frac{2 \times (1.54 \times 10^{-8}) \times 0.5}{1} \] \[ \lambda = (1.54 \times 10^{-8}) \text{ cm} \]