Download 1 - barnes report

1. Units for length and energy
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.
2. Typical energies involved in studies of solids
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=
3. 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?
1. Units for length and energy
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.
Answer:
1 eV = 1.602 10-19 Coul Volt = 1.602 10-19 J
1 J = 0.6227 1019 eV
2. Typical energies involved in studies of solids
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:
Answer:
In SI units: = h = 6.626 10-34 J s; me = 9.109 10-31 Kg; mN = 1.675 10-27 Kg = 1840
me; c = 2.998 108 m/s
The needed quatities are: Photons
E=pc = hc/lambda = 1.986 10-25 J m/lambda = 1.237 10-6 eV (m/lambda) = 1.237
103 eV (nm/lambda)
For particles with mass (non-relativistic) E = p2/2m = (h2/2m)(1/lambda2)
For electrons: (h2/2me) = 43.90 10-68 J2/ (2 x 9.109 10-31 Kg) = 2.100 10-37 J
(m2/lambda2) = 1.500 10-18 J (m2/lambda2) = 1.500 eV(nm2/lambda2)
For neutrons the energies are divided by the factor 1840
particle
electron
lambda = 0.1 nm
E= 1.50 102 eV
-2
lambda = 1.0 nm
E= 1.50 eV
neutron
E= 8.16 10 eV
E= 8.16 10-4 eV
photon
E= 1.237 104 eV
E= 1.237 103 eV
3. 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?