Question

Wavelength of X-rays used in a diffraction experiment is 1.54 Å. X-rays are diffracted from a set of planes with an interplanar spacing of 1.54 Å. Then the angle θ (in degrees) corresponding to the first-order Bragg diffraction is

• A. 30º
• B. 15º
• C. 45º
• D. 90º

Answer 1

The Correct Option is A

• Using Bragg’s law:

\( n\lambda = 2d \sin \theta \)

• For the first-order diffraction (n = 1):

\( \lambda = 1.54 \text{ ˚A}, \quad d = 1.54 \text{ ˚A} \)

• Substituting into Bragg’s law:

\( \sin \theta = \frac{\lambda}{2d} = \frac{1.54}{2 \times 1.54} = \frac{1}{2} \)

The angle corresponding to \(\sin \theta = \frac{1}{2}\) is:

\( \theta = \arcsin \frac{1}{2} = 30^\circ \)

Thus, the angle θ for the first-order Bragg diffraction is 30◦.