X-ray diffraction and Bragg's law (introductory)
Diffraction · Physics
Study notes
Problem: An X-ray with a wavelength of 0.154 nm is incident on a crystal with a spacing of 0.200 nm between atomic planes. Find the angle of incidence (theta) for the first-order maximum (n=1). Step 1: Identify the given values. Wavelength (lambda) = 0.154 nm Interplanar spacing (d) = 0.200 nm Order (n) = 1 Step 2: Use Bragg's Law formula. The formula is: 2 * d * sin(theta) = n * lambda Step 3: Rearrange the formula to solve for sin(theta). sin(theta) = (n * lambda) / (2 * d) Step 4: Substitute the values. sin(theta) = (1 * 0.154) / (2 * 0.200) sin(theta) = 0.154 / 0.400 sin(theta) = 0.385 Step 5: Calculate the angle theta. theta = arcsin(0.385) theta ≈ 22.6 degrees. So, the angle of incidence is approximately 22.6 degrees.