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# The Solid State

## Problems

All diagrams must be hand drawn, no photocopies or computer images will be accepted.

1. Light with wavelength in the range of 400 to 750 nm (1 nm = 10-9 m) are visible, whereas wavelength of X-rays are about 0.5 to 0.001 nm. According to Max Planck's assumption, the energy E of a photon with frequency v is E = h v, where h is the Planck's constant. The frequency v is related to the speed of light c, and wavelength l by v = c / l. Calculate the frequencies and energies of the photons with the four wavelengths indicated above. (h = __, c = __)

__ (show calculation for one, and results for all below)

```Wavelength  v         E
/ nm       /Hz       /J per photon
400        __        __
750        __        __
0.5        __        __
0.001      __        __
```

X-rays of what wavelength will be suitable for structural investigation? Please recall the bond distances for diamond and silicon from Assignment 3 for consideration.

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2. Packing of spheres are used to model the structures of solids. Provide information on the following questions based on this model.

Draw pictures to show the two types of packing sequences ABAB... and ABCABC....

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Draw pictures to show spheres around an octahedral (O) and a tetrahedral (T) holes or sites.

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Calculate the radii of the largest spheres that will fit in the octahedral and tetrahedral hole without pushing the large spheres apart. Assume the radii of the spheres around the holes to be 1.000 nm.

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Draw a cubic unit cell of the face-centered closest packing (fcc), and mark the layers of packing sequense ABCABC... etc.

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Classify these metals according to their structure types: copper, silver, gold, zinc, cadmium, sodium, potassium, and rubidium.

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3. Describe the sodium chloride and zinc blend structures and their relation ship with the closest packing models. What are the differences between the zinc blende (sphalerite) and wurtzite structures?

The purpose of these comparisons is to entice you to these topics: