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In this lesson, we will learn how to 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 AΜ apart produces a first-order reflection at π = 7 . 7 5 β . Calculate the difference in energy between the L and K shells of the molybdenum atom.

Q2:

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

Q3:

Platinum crystallizes with a face-centered cubic unit cell and diffracts X-rays of wavelength 1.541 AΜ to produce a second-order ( π = 2 ) reflection at 2 π = 4 6 . 2 5 β . Calculate to 3 significant figures the density of platinum.

Q4:

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

Q5:

When X-rays of wavelength 1.541 AΜ are diffracted by a crystal, the first-order reflection occurs at angle π = 1 5 . 5 5 β . Calculate to 3 significant figures the spacing of the crystal planes that give rise to this reflection.

Q6:

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

Q7:

When X-rays of wavelength 0.2287 nm are diffracted by a crystal, the first-order reflection occurs at angle 2 π = 3 9 . 2 1 β . Calculate to 3 significant figures the spacing of the crystal planes that give rise to this reflection.

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