Final answer:
The student's question is about applying Bragg's Law to find the diffraction angle in a crystal structure when a neutron beam is used. It requires knowledge of the neutron beam wavelength and the crystal's interlayer spacing to calculate the angle of the first-order diffraction peak.
Step-by-step explanation:
The question involves determining the observed angle (2θ) for diffraction in a crystalline solid when a neutron beam with a wavelength of 2.567 Angstroms is used, and the interlayer distance in the crystal is 3.325 Angstrom. This is a classic example of applying Bragg's Law, which is used in X-ray diffraction experiments to find the angles at which constructive interference of the reflected waves occurs, providing information about the crystal structure.
Bragg's Law is given by:
nλ = 2d sin(θ)
Where:
- n is the order of the diffraction peak (n = 1 for first-order diffraction)
- λ is the wavelength of the incident beam
- d is the spacing between the planes in the crystal
- θ is the angle between the incident ray and the planes in the crystal, and 2θ is the total diffraction angle observed
In this scenario, assuming first-order diffraction (n=1), the Bragg's Law equation becomes:
2.567 = 2 × 3.325 sin(θ)
By solving for θ, we can determine the angle 2θ that corresponds to the observed diffraction peak.