Question

X rays difract from a crystal in which the spacing between atomic planes is 0.162 nm. The secondorder difiraction occurs at 46.0∘. What is the angle of the first-order diffraction? Express your answer in degrees.

Answer 1

The angle of the first-order diffraction for a crystal where the second-order diffraction occurs at 46.0° is 23.0 degrees, which is simply half of the second-order angle.

Step-by-step explanation:

The angle of the first-order diffraction for X-rays diffracting from a crystal can be calculated using Bragg's law, which states that nλ = 2d sinθ, where n is the order of diffraction, λ is the wavelength, d is the spacing between atomic planes, and θ is the diffraction angle.

Given that the second-order diffraction occurs at 46.0°, we can deduce the angle for the first-order diffraction. Since the second order is n=2 and the angle is twice that of the first order, we simply halve the second-order angle to find the first-order diffraction angle.

Therefore, the angle for the first-order diffraction is 23.0 degrees.