A given crystal structure (such as NaCl) can be represented as consisitng of pla
ID: 2133561 • Letter: A
Question
A given crystal structure (such as NaCl) can be represented as consisitng of planes of atoms, as shown in the figure. A beam of x-rays can be reflected off the crystal, where some of the beam penetrates through the atoms of the upper layer and strikes the atoms in the lower plane. A pair of incident x-rays from an x-ray source is reflected from the crystal as shown and into an x-ray detector.
a) How much farther does the beam reflected from the lower plane travel from the source to the detector than the one reflected from the upper plane?
b) If the beams have wavelenth, lambda, under what conditions will the two reflected beams constructively interfere with each other (i.e. have maxima at the same points)?
c) The relationship you derived in part (b) was first derived by W.L. Bragg. If we can experimentally measure the diffraction angle and we know the wavelength used, what feature of the crystal can we use this relationship to determine?
A given crystal structure (such as NaCl) can be represented as consisitng of planes of atoms, as shown in the figure. A beam of x-rays can be reflected off the crystal, where some of the beam penetrates through the atoms of the upper layer and strikes the atoms in the lower plane. A pair of incident x-rays from an x-ray source is reflected from the crystal as shown and into an x-ray detector. How much farther does the beam reflected from the lower plane travel from the source to the detector than the one reflected from the upper plane? If the beams have wavelenth, lambda, under what conditions will the two reflected beams constructively interfere with each other (i.e. have maxima at the same points)? The relationship you derived in part (b) was first derived by W.L. Bragg. If we can experimentally measure the diffraction angle and we know the wavelength used, what feature of the crystal can we use this relationship to determine?Explanation / Answer
1. Beam reflected from lower plane travels an extra distance of 2*sin(q).
2. For constructive interference, the condition should that, the extra distance 2*sin(q)=(m)*(lambda), where m is an integer.
3. The inter-planar distance in a crystal. Its actually the perpendicular distance b/w successive planes. In this case, it is d.
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