Phys 460 Homework # 0

A convenient unit of length for description of solids is the nanometer (nm), which is the order of magnitude of a typical distance between atoms. (Actual sizes are between 0.1 nm and 1.0 nm. Many older texts use the Angstrom = 0.1 nm.) A convenient unit of energy is the electron volt (eV), which is the energy gained by moving an electron through a potential difference of 1 volt. Give the relation of between an EV and the standard SI unit of energy, the Joule.

Solids are made of nuclei and electrons. Much of our information about solids is found by studying them using other particles like light (photons) and neutrons. According to the laws of quantum mechanics, all particles act like waves and waves act like particles, with the relation lambda = h/p, where lambda is the wavelength, p is the momentum, and h is Planck's constant. The relation of energy and momentum for particles like electrons and neutrons is E = p²/2m, and for photons is E = pc. Give the energies in eV for each of the particles below for the wavelength shown:

particle	lambda = 0.1 nm	lambda = 1.0 nm
electron	E=	E=
neutron	E=	E=
photon	E=	E=

Symmetry in crystals

One of the beautiful qualities of solids is that they are often crystals of extraordinary regularity and shape. This will be one of the first subjects of the course. There are also other regular patterns one sees often, e.g., tile on a floor. Below are three figures of typical tile patterns. Imagine that each pattern extends to infinity in all directions. (Ignore distortions in the patterns that are caused by the printer and the browsers.)

Describe any symmetries that you see in each of the patterns. (Use a separate sheet if needed.) For example, the pattern on the top left is the same if it is rotated by 180 degrees. Thus it is symmetric under 180 degree rotations. Are there other rotations that leave the pattern the same? Are there reflections that leave the pattern the same, i.e., if a mirror were placed vertically on the floor in a certain orientation, would the pattern look the same in the mirror?