The silicon wafer is coated with a layer of metallic aluminum which acts as an electrical contact. The x-ray diffraction pattern of aluminum is measured in a diffractometer with Fe Kα radiation. At what angle, θ, do you expect to observe the first reflection of aluminum, i.e., the reflection at the lowest angle? Express your answer in degrees.

Use lamba = 2d*sin(theta)

d is the distance between planes in Al and I don't know d. You can look up K alpha for Fe and d for Al.

13.8 Many thanks. I see now :)

It's wrong.

What's the answer?

To determine at what angle the first reflection of aluminum would be observed in the x-ray diffraction pattern, we need to consider the Bragg's Law.

Bragg's Law is given by the equation:

n * λ = 2 * d * sin(θ)

where:
- n is the order of the reflection (in this case, it is the first reflection, so n = 1)
- λ is the wavelength of the incident x-ray radiation (Fe Kα radiation has a wavelength of 1.937 Å)
- d is the interplanar spacing of the crystal lattice planes (for aluminum, it is 2.052 Å)
- θ is the angle of reflection that we want to determine

Rearranging the formula, we can solve for θ:

θ = arcsin((n * λ) / (2 * d))

Substituting the values, we get:

θ = arcsin((1 * 1.937 Å) / (2 * 2.052 Å))

Calculating this, we find:

θ ≈ 15.7 degrees

Therefore, we expect to observe the first reflection of aluminum at an angle of approximately 15.7 degrees in the x-ray diffraction pattern.