Final answer:
The spacing of the crystal is approximately 1.89 Å.
Step-by-step explanation:
The spacing of the crystal can be determined using the Davisson-Germer experiment formula, which states that nλ = asinθ, where n is the order of the maximum, λ is the wavelength of the incident radiation, a is the lattice spacing, and θ is the glancing angle. In this case, the first reflection maxima occurs at a glancing angle of 60°. Given that the incident radiation wavelength is 1.64 Å and the glancing angle is 60°, we can rearrange the formula to solve for a:
a = (λ/sinθ)
Substituting the values:
a = (1.64 Å / sin(60°))
Simplifying further:
a ≈ 1.89 Å
So the spacing of the crystal is approximately 1.89 Å.