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 . 7 5 . 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 2 𝜃 = 4 6 . 2 5 . 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.

Q5:

When X-rays of wavelength 0.2287 nm are diffracted by a crystal, the first-order reflection occurs at angle 2 𝜃 = 3 9 . 2 1 . 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 = 1 5 . 5 5 . 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-centred 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.

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