Midterm 1: Bonding and Crystallography Fundamentals; The valence electron configuration of carbon is; The De Broglie wavelength is? How many electrons can occupy the 4f or- bitals? In the hydrogen atom the energy of orbitals is dictated by the quantum number?

• The De Broglie wavelength is:
  • A property of all matter
  • Only a property of electrons because of the Schödinger wave equation
  • Only a property of electrons, photons and phonons

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1. Concept questions: (1 point each, 15 points total)
   • Which of the folowing is not a valid combi- nation of quantum numbers for an atomic or- bital:

a)  n = 2, l = 1,m =   1

(b) n = 1, l = 0,m = 0

(c) n = 1, l = 1,m = ≠1

• The De Broglie wavelength is:
  • A property of all matter
  • Only a property of electrons because of the Schödinger wave equation
  • Only a property of electrons, photons and phonons
• The valence electron configuration of carbon is:
  • ns2 np2
  • ns2
  • (n ≠ 1)d1 ns2
• How many electrons can occupy the 4f or- bitals?
  • 14
  • 10
  • 7
• Covalent bonds are generally:
  • Stronger than metallic bonds
  • Softer than metallic bonds
  • Melt at a lower temperature than metal- lic bonds
• In the hydrogen atom the energy of orbitals is dictated by the quantum number:
  • n + l
  • n only
  • n (n + 1)
• A metallic bond is predominantly:
  • Strongly directional
  • Completely non-directional
  • Partly directional
• A glass is characterized by:
  • Long-range order and short-range order
  • Completely disordered
  • Short-range order but no long-range or- der
• An cation is:
  • An atom that has lost a small number of electrons
  • An atom that has gained a small number of electrons
  • A charged atom that looks like a cat
• The wave function of an electron in atomic orbital has a well defined:
  • Wave vector
  • Kinetic energy
  • Total energy
• The wave function of an electron in atomic orbital has a radial dependence, r, that far from the nucleus scales as:

r

• ≥ 1
• ≥ e^≠r/ro
• ≥ cos(kr)

 

• The lattice vectors of a crystal define:
  • The unit cell
  • The crystal structure
  • The atom positions

 

• A face-centered (F) unit cell contains:
  • One lattice point

• Two lattice points
• Four lattice points
• A tetragonal unit cell has:
  • a = b = c
  • a = b ”= c
  • a ”= b ”= c
• The Miller indices (hkl) represent:
  • A single plane in a crystal structure
  • A set of parallel planes in a crystal struc- ture
  • family of planes related by symmetry in a crystal structure

 

 

2. Compute the DeBrogli waves length of the following (1 point each)
   • An electron accelerated through a potential of 5 ◊ 106 volts

 

• A cricketball (160 g) with kinetic energy of 149 J

 

• A He atom with thermal energy at T = 300 K

(The average kinetic energy per degree of freedom at temperature T  is E_K =  kB2T )

Bonus question: What is wrong with the answer in (b)? and why is this the case? (1 point)

 

3. What are the frequencies and wavelengths of the photons emitted from a hydrogen atom when an electron makes a transition from state n = 5 to the lower level n = 3 ? (6 points) NB: consider all the paths the electron could

 

4. Crystal systems: For each of the wallpaper patterns below identify and draw the (I) translation vectors,

(II) the primitive cell and unit cell unit cell, (III) the Wigner-Seitz cell, and then (IV) name the patterns’ (2D) bravais lattice type. (16 points)

 

È     Í                                !      ”         !      ”                                                     )        *

• Miller indicies: Draw in the axes below the following planes and In the cubic crystal: (left)

102  , and (right) planes   1¯12   and   ¯120  .  In the hexagonal crystal:  (left)  10¯11  , and (right) the directions #¯2112$ and #10¯12$. Be sure to indicate which is which. (8 points)

 

6. Crystal metrics: a trigonal (rhombohedral) crystal system has an angle of 46.5¶ between the [100] and

[111] directions.

!      “

• What is the angle – between the lattice vectors? (Hint: use the lattice’s metric tensor) (5 points)
• Of the (110) and   1¯10   planes in this crystal system which have the largest plane spacing?  (5 points)

 

!        ” !        “

• Crystal metrics: The equilibrium shape of a crystal is dictated by the energy of its low index crystal facets, and so one can often identify facet types just by looking at the symmetry of a crystal and the relative angles between For a hexagonal crystal with a ratio of lattice parameters c/a = 1.65:
• compute the angles between each pair of the following set of planes the 10¯12  ,  2¯1¯12  , and (0001)

planes. (9 points)

• Identify the )10¯12*, )2¯1¯12*, and {0001} type facets on the crystal belo (3 points)

8. You have synthesized a new material, in your lab — it is catalyst for solar splitting of You are excited, it give the world unlimited clean energy, it will save the environment, and you will get very rich doing it! Your computational collaborator predicts that this material should be simple cubic. You perform and powder x-ray diffraction measurement and obtain low 2◊ scattering peaks the following angles: 2◊ = 11.96¶, 14.36¶, 18.73¶, 20.36¶, and 25.01¶. As you can immediately tell these are inconsistant with a cubic material. This could mean that there is a second phase mixed in with the cubic phase, or it could be that you do not have the cubic phase at all. Inspect the data and determine which it is: do you need to go back to the lab, or can start thinking about which yacht you are going to buy? (8 points)

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