Worksheet: Bragg's Law

In this worksheet, we will practice derive Bragg's law and use this formula to calculate lattice spacings, scattering angles, and radiation wavelengths.

Q1:

When an electron in an excited atom of molybdenum relaxes from the L-shell to the K-shell, an X-ray photon is emitted. Diffraction of this light by layers of atoms 2.64 Å apart produces a first-order reflection at 𝜃=7.75. Calculate the difference in energy between the L- and K-shells of the molybdenum atom.

Q2:

X-rays of wavelength 0.5594 Å are diffracted by a face-centred cubic metal lattice. The radius of the metal atom is 1.345 Å. Calculate to 3 significant figures the diffraction angle 𝜃 of the second-order (𝑛=2) reflection.

Q3:

Platinum crystallizes with a face-centered cubic unit cell and diffracts X-rays of wavelength 1.541 Å to produce a second-order (𝑛=2) reflection at 2𝜃=46.25. Calculate to 3 significant figures the density of platinum.

Q4:

X-rays of wavelength 0.2879 nm are diffracted by a crystal with a layer spacing of 4.164 Å. Calculate to 3 significant figures the diffraction angle 𝜃 of the first-order reflection.

  • A 2 3 . 7
  • B 2 3 . 5
  • C 2 0 . 4
  • D 2 1 . 9
  • E 2 5 . 0

Q5:

When X-rays of wavelength 0.2287 nm are diffracted by a crystal, the first-order reflection occurs at angle 2𝜃=39.21. Calculate to 3 significant figures the spacing of the crystal planes that give rise to this reflection.

Q6:

When X-rays of wavelength 1.541 Å are diffracted by a crystal, the first-order reflection occurs at angle 𝜃=15.55. Calculate to 3 significant figures the spacing of the crystal planes that give rise to this reflection.

Q7:

X-rays of wavelength 1.936 Å are diffracted by a body-centered cubic metal lattice. The radius of the metal atom is 1.260 Å. Calculate the diffraction angle 𝜃 of the second-order (𝑛=2) reflection in degrees to 3 significant figures.

Q8:

X-rays of wavelength 0.1057 nm are diffracted by a cubic metal lattice, producing a second-order (𝑛=2) reflection at 2𝜃=36.67. The metal atom has a radius of 1.680 Å and molar mass of 210 g/mol. Calculate the density of the metal to 3 significant figures.

  • A9.19 g/cm3
  • B18.4 g/cm3
  • C4.58 g/cm3
  • D18.3 g/cm3
  • E2.29 g/cm3

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