Final answer:
The expected diffraction angle for a crystal with a plane spacing of 0.394 nm and X-ray wavelength of 0.147 nm is determined by rearranging the Bragg equation for the angle θ and solving for it.
Step-by-step explanation:
To determine the expected diffraction angle of an X-ray interacting with a crystal, we use the Bragg equation:
nλ = 2d sin(θ)
Where n is the order of diffraction, λ is the wavelength of the X-ray, d is the spacing between the planes in the crystal, and θ is the diffraction angle.
Let's solve the given problem:
- For a crystal with a plane spacing of d = 0.394 nm
- Using an X-ray with a wavelength of λ = 0.147 nm
- Considering the first order diffraction (n = 1)
The Bragg equation will be:
1×0.147 nm = 2×0.394 nm sin(θ)
Upon solving for θ, we find the expected diffraction angle for the first order diffraction.