X-Ray Diffraction and the Bragg Condition · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Reading atomic spacing from X-ray spots

Science · Waves, Light & Sound · ages 20-22
Name ______________________   Date ____________

  1. 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

  2. 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

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

    Circle one:   True   False

  4. 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

  5. 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?

    Answer: ______________

  6. 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

  7. 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

  8. 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
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Reading atomic spacing from X-ray spots W1-mt_qEDplGeIkB-s1

  1. X-ray wavelengths suit atomic spacings; visible wavelengths are too long · The Bragg condition needs n lambda <= 2d. X-ray wavelengths can meet that bound for atomic spacings; visible wavelengths cannot.
  2. n lambda = 2d sin(theta), with theta measured from the diffracting planes · Rays from adjacent planes have a path difference of 2d sin(theta). Constructive interference requires that path difference to equal n wavelengths.
  3. False · Theta is measured from the diffracting planes, not their normal. Those planes need not be parallel to the sample surface.
  4. It moves to a smaller glancing angle as spacing increases · With wavelength and order fixed, sin(theta) = n lambda/(2d). A larger d gives a smaller sine and a smaller theta.
  5. 0.36 · d = n lambda/(2 sin(theta)) = 2 x 0.180/(2 x 0.5) = 0.360 nm.
  6. Positions constrain lattice geometry; intensities depend on atomic contributions · Positions constrain spacings and lattice geometry. Intensities depend on interfering atomic contributions, but do not directly provide their phases.
  7. The required n lambda/(2d) cannot exceed 1, since it equals sin(theta) · An order needs sin(theta) = n lambda/(2d) <= 1. Equality gives theta = 90 degrees; a larger required value has no angular solution.
  8. Periodic scattering reinforces selected directions, rather than all directions equally · The crystal's repetition causes strong constructive interference in selected directions. Peaks have finite width, and some background may remain.
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