Problem 1
Pentene is a molecule with the chemical formula C5H10. The carbon atoms form a chain. There are different isomers possible. Isomers have the same chemical formula but different shapes. Draw any pentene isomer indicating where the sigma and pi bonds are.
How can you determine which isomer is most likely to be observed?
Problem 2
The conventional uniti cell of CsCl is shown below. Take the cube edge length to be $a$.
(a) What is the Bravais lattice type?
(b) What is the volume of the primitive unit cell?
(c) What are the primitive reciprocal lattice vectors for this crystal?
Problem 3
The lattice constants for a hexagonal metal have the relationship $c=2a$. Some distances in the first Brillouin zone are given below.
Use the empty lattice approximation to draw the lowest band of the electronic band structure in the directions $A-\Gamma-M-K$.
Sketch the electron density of states near the bottom of the band you have drawn.
Problem 4
By applying stress to a semiconductor, the resistance can be changed. This is called the piezoresistive effect. A change in the arrangement of the atoms in the crystal due to stress will change the band structure.
(a) How can you measure the change in the arrangement of the atoms experimentally?
(b) How will the resistance change if the curvature of the conduction band minimum gets sharper? Why?
(c) How will the resistance change if the band gap of the semiconductor increases? Why?