Why are X-rays suitable for diffraction from atomic planes spaced about 0.1 nm apart, while visible light is not?

• X-rays produce sharper patterns because they move faster than visible light
• Visible light is completely absorbed by all crystals and never scatters
• X-ray wavelengths suit atomic spacings; visible wavelengths are too long

Which equation is the Bragg condition? Here n is a positive integer order, lambda is wavelength and d is plane spacing.

• n lambda = d sin(theta), with theta measured from the diffracting planes
• n lambda = 2d sin(theta), with theta measured from the diffracting planes
• n lambda = 2d cos(theta), with theta measured from the diffracting planes

In n lambda = 2d sin(theta), theta is measured from the normal to the diffracting lattice planes.

For the same X-ray wavelength and diffraction order, how does increasing plane spacing change the glancing angle of an allowed reflection?

• It moves to a smaller glancing angle as spacing increases
• It moves to a larger glancing angle as spacing increases
• It remains at an unchanged glancing angle as spacing increases

X-rays of wavelength 0.180 nm give a second-order reflection at theta = 30 degrees to the lattice planes. What is the plane spacing in nm?

Which statement correctly distinguishes diffraction positions from intensities?

• Positions depend only on atom types; intensities depend only on lattice spacings
• Positions constrain lattice geometry; intensities depend on atomic contributions
• Positions give atomic phases; intensities alone give unique atomic coordinates

For fixed plane spacing d and wavelength lambda, what geometrically limits the positive diffraction orders permitted by Bragg's law?

• The required n lambda/(2d) cannot exceed 1, since it equals sin(theta)
• The allowed order must stop at n = 3, independent of spacing and wavelength
• The wavelength must equal d exactly, regardless of order or measured angle

For an oriented single crystal, why is an even diffraction glow not the expected pattern?

• Every incident X-ray is absorbed by the crystal, leaving no scattered rays to form spots
• The detector creates sharp spots by grouping an otherwise uniform scattered intensity
• Periodic scattering reinforces selected directions, rather than all directions equally