Solid State Physics 1

PHYS3710

Question Bank

---------------------------------------------------------------------------------Multiple-choice questions

1. Condensed Matter is:a. Solidsb. Liquidsc. Solids and Liquidsd. Gasses and Liquids

2. A Crystalline Solid is the solid form of a substance in which the atoms or molecules:a. are arranged in a definite structureb. are arranged in repeating pattern in three dimensionsc. are arranged in regular patternsd. all the above

3. Glasses are:a. Crystalline solidsb. Amorphous solidsc. Polycrystalline solidsd. None of the above

4. Real Crystals could have atoms in between lattice sites where they should not be. These atoms called:a. Latticeb. Impuritiesc. Vacanciesd. Interstitials

5. A Crystal Lattice is:a. A 3-dimensional periodic array of atoms.b. An idealized description of the geometry of a crystalline materialc. Crystal with no defects.d. Crystal that never occurs in nature

6. Atomic Mass (A) is:a. Sum of the masses of protons and neutrons within the nucleusb. No. of electronsc. Mass of protonsd. Mass of neutrons

7. Electron configuration of the following element is not stable:a. 1s2

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b. 1s22s22p2

c. 1s22s22p6

d. 1s22s22p63s23p6

8. Metallic bonding are:a. Have a few free electrons.b. Directionalc. Very strongd. Good electrical and heat conductors

9. Materials with covalent bonding are characterized by:a. Electrically and thermally insulative.b. High electrical conductivityc. High thermal conductivityd. Low melting temperature

10. Based on the following energy-ro diagram choose the correct answer below (A and B are different materials):a. A has larger thermal expansion coefficient than Bb. A has larger E Modulus than Bc. B has larger melting temperature than Ad. B has larger bonding Energy than A

11. Waves which propagate through a material medium (solid, liquid, or gas) are called:a. Longitudinal wavesb. Transverse wavesc. Electromagnetic wavesd. Mechanical waves

12. Wave diffraction usually changes a. The direction and shape of the wave. b. The frequency of the wave. c. The length of the wave. d. The type of the wave.

13. Monoatomic Chain is:a. The simplest crystal model, which is the one dimensional chain of identical

atoms.b. The waves add up to make a wave with smaller or zero amplitude.c. The phase velocity.d. The shorter (blue) wavelengths refracted more than long (red) wavelengths.

14. X-Ray are:a. Mechanical wavesb. Electromagnetic wavesc. Sound wavesd. Transverse waves

15. If an electron drops to a lower orbital (spontaneously or due to some external perturbation) it releases some energy. This released energy is in the form of:

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a. A photona. A phononb. Radiationc. Wave

16. The following Figure represents:a. Body Centered Cubic Wigner-Seitz Cellb. Face Centered Cubic Wigner-Seitz Cellc. Body Centered Cubic Primitive Celld. Face Centered Cubic Bravais cell

17. Primitive Unit Cell is:a. Composed from 1 atom.b. Composed from lattice and atoms or

molecules.c. The smallest component of the crystal, which, when stacked together, reproduces

the whole crystald. All of the above.

18. Coordination number in SC is:a. 2b. 4c. 6d. 8

19. Which of the following statements is false?a. Solids require the same energy to break the interatomic bonds as liquids.b. Solids require more energy to break the interatomic bonds than liquids.c. Solids require less energy to break the interatomic bonds than liquids.d. There is no relation between energy and interatomic bonds.

20. Nondirectional bonding refer to:a. Bond magnitude is equal in all directions around an ion.b. Non ionic bonding.c. Covelent bonding.d. Stable valence electrons.

21. Which of the following structures are/is a primitive unit cell: Simple cube ( SC) , Body centered cube (BCC) , and Face centered cube (FCC)?a. BCC and FCCb. SC and FCCc. SCd. None

22. Lattice structure is:a. A lattice and basisb. A real crystalc. A perfect crystald. Atoms

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23. Here is the energy diagram against the interatomic separation between two atoms. Which of the atoms (1,2,3, or 4) have the most stable position regarding to the positive ion on point zero?a. 1b. 2c. 3d. 4

24. The following Figure shows the atomic arrangements of different unit cells choices, primitive unit cells are:

a. A,B,Cb. A,B,Ec. A,C,Fd. C,D,F

Based on the electronegativity table, as shown below, circle the correct answers (questions 6 and 7):

25. Which is the most ionic bond of the following compounds:a. NaClb. H2Oc. CH4

d. O2

26. Which is the most covelent bond of the following compounds:a. CaOb. CO2

c. Cs2O d. BaBr2

27. The number of atoms per unit cell of BCC (Body Centered Cube) lattice is?a. 1b. 2c. 4d. 8

28. Angle of incidence is:a. The angle between the surface and the incident light.b. The angle between the normal and the incident light.c. The angle between the incedent and the reflected light.d. The angle bewteen the two parallel rays

29. The bright & dark lines from the diffraction experiment can only be explained:a. Interfernce of two slits. b. Waves cancelling each other out.c. Wave peaks can add together

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d. Constructive and destructive interference pattern 30. X-Rays are:

a. Mechanical waves, invisible light.b. Electromagnetic Radiation.c. Mechanical waves , visible ight.d. High energy mechanical wave.

31. X-Ray photons pass through most things because: a. They have too much energyb. They don't have enough energyc. They are diffracted.d. They have long wavelength.

32. Diffraction of radiation from the lattice occurs when:a. The wavelength of the radiation is larger than the lattice constant.b. The wavelength of the radiation is larger than the interatomic spaces.c. The wavelength of the radiation is smaller than the electrond. The wavelength of the radiation is comparable or smaller than the lattice constant.

33. A 3rd order reflection from the (111) plane is:a. (113)b. (131)c. (333)d. (311)

34. The X-Ray Diffractıon method using polycrystal is:a. Laueb. Powderc. Rotating angled. a and c

35. The number of atoms per unit cell of FCC (Face Centered Cube) lattice is?a. 1b. 2c. 4d. 8

36. The following figure shows the crustal structure of snow the number of symetrical folds around the central axis is:a. 1b. 2c. 4d. 6

37. Phonon is:a. Electromagnetic Energyb. A Lump of Vibrational Energyc. X-raysd. Crystalline material

38. W (angular frequency) is:

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a. 2 πfb. 2πT

c. 2 πλ

d. Mv39. Which figure represents Hooke's law:

40. The number of atoms per unit cell of SC (Simple Cube) lattice is?a. 1 b. 2c. 4d. 8

41. The following diagram represents the lattice points of crystal. Accordingly, the primitive unit cell is numbered with:a. 1b. 2 c. 3d. 4

42. From previous diagram, the non-unit cell is:a. 1b. 2c. 3 d. 4

43. If the following diagram represents the lattice and basis, then the crystal structure is:

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44. The following diagram represents the potential energy curve of two materials. Based on this diagram which of the following is true sentence?

a. Material 2 exhibits higher E Modulus than Material 1b. Material 2 exhibits higher melting temperature than

Material 1c. Material 2 exhibits higher thermal expansion than

Material 1d. None of the above is correct

45. Which of the following is not representing a unit cell:a. ab. bc. cd. d

46. The following Bravais lattice in 2D is called: a. Centered rectangularb. Rectangularc. General or Obliqued. Hexagonal

47. The number of atoms per unit cell of BCC (Body Centered Cube) lattice is?a. 1b. 2c. 4d. 8

48. Which of the following figures represents S orbital?

49. The following figure represents the unit cell in 3D of:

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a. Simple cube structureb. Body centered cube structurec. Face centered cube structure

50. The symmetry of plane lattice is called:a. Inversionb. Reflectionc. Rotation

51. Ohm’s law valid for:a. Metalsb. Ceramicsc. Polymersd. All materials

52. Wiedemann and Franz found that:a. The ratio of thermal and electron wavelength for all metals is constant at a given

temperatureb. The ratio of thermal and electron wavelength for all metals is constant at a given

temperaturec. The ratio of thermal and electrical conductivity for all metals is constant at a

given temperatured. The ratio of thermal and electrical conductivity for all materials is constant at a

given temperature53. The closed-packed structure of FCC is:

a. AAAAb. ABABABABc. ABCABACABCd. ABCDABCDABCD

54. The primitive unit cell in the following lattice structure is:a. 1b. 2c. 3d. 4

55. a large electronegativity difference is required for:a. Ionic bondingb. Covalent bondingc. Metallic bondingd. Van der Waals bonding

56. The chemical bonding in Iron isa. Ionicb. Covalentc. Metallicd. Van der Waals

57. The following figure represents:a. A single crystal

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b. Polycrystallinec. Amorphous

58. The following figure shows the electronic band structure of an element. Accordingly, this element is:a. Conductorb. Semiconductorc. Insulator

59. If the wavelength of a wave on a string is 1 meter and its speed is 5 m/s, then the frequency of the wave is:a. 1 HZb. 0.2 HZc. 5 HZd. 10 HZ

60. The following figure shows the reflection of X-rays from a crystal, the d-spacing is numbered by:a. 1b. 2c. 3d. 4

61. Close Packing sequence of simple cubic (SC) structure is:a. AAAA ….b. ABAB….c. ABCABC….

62. A reflection symmetry of a lattice is occurs by:a. Pointb. Axisc. Planed. Crystal

63. The number of folds around the axis as shown in the next figure is:a. 1b. 2c. 3d. 4

64. The following wave is considered:a. Electromagneticb. Transversec. longitudinal d. Short

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65. The wave length of the X-rays is around:

a. 10-6mb. 10-9mc. 10-10md. 10-12m

66. If the following figure represents a crystal structure, then the basis contains: a. One atomb. Two atomsc. 4 atomsd. 9 atoms

67. The electron configuration of some elements is shown below. Which of these elements is stable?

a. 1s1

b. 1s2

c. 1s22s1

d. 1s22s2

68. According to the periodic table, Mg is readily to give up:a. 1 electronb. 2 electronsc. 3 electronsd. 4 electrons

69. The following lattice represents:a. Ideal and non-Bravais crystalb. Real and no-Bravais crystalc. Real and Bravais crystald. Ideal and Bravais crystal

70. The primitive unit cells in the following lattice structure are:a. 1 and 2b. 2 and 3c. 3 and 4

71. The following figure shows the electron band structure of diamond. Accordingly, the forbidden energy gap of carbon in diamond structure is:a. 7.0 evb. 1.0 ev c. 0.01 ev                            d. none 

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Questions1. The wavelength of a wave on a string is 1 meter and its speed is 5 m/s. Calculate the

frequency and the period of the wave.

2. Determine the ionic character % of MgO, where the electronegativities are: XMg = 1.3 and XO = 3.5

3. Calculate the Atomic Packing Factor of Body Centered Cubic (BCC) Lattice? 4. Find the direction of the arrows as shown in the following crystals:

5. Find Miller indices of the following crystal plane?

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6. For BCC iron, compute (a) the interplanar spacing, and (b) the diffraction angle for the (220) set of planes. The lattice parameter for Fe is 0.2866 nm. Also, assume that monochromatic radiation having a wavelength of 0.1790 nm is used, and the order of reflection is 1.

Solution: (a) The value of the interplanar spacing is determined, with a= 0.2866 nm, and h= 2, k = 2, l = 0, and since we are considering the (220) planes. Therefore,

(b) The value of ɵ may now be computed, with n=1 since this is a first-order reflection:

The diffraction angle is 2ɵ or:

7. Determine the atomic Packing Factor (APF) of Simple cube cell?

8. Determine the atomic Packing Factor (APF) of BCC cell?

9. 1. Determine the atomic Packing Factor (APF) of FCC cell?

10. The metal rhodium has an FCC crystal structure. If the angle of diffraction for the (311) set of planes occurs at 36.12o (first-order reflection) when monochromatic x-radiation having a wavelength of 0.0711 nm is used, compute (a) the interplanar spacing for this set of planes, and (b) the atomic radius for a rhodium atom.

Solution:

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a

bc

2

2

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From the data given in the problem, and realizing that 36.12° = 2θ, the interplanar spacing for the (311) set of planes for rhodium may be computed using the following Equation:

In order to compute the atomic radius we must first determine the lattice parameter, a, and then R , since Rh has an FCC crystal structure. Therefore,

11. The metal niobium has a BCC crystal structure. If the angle of diffraction for the (211) set of planes occurs at 75.99o (first-order reflection) when monochromatic x-radiation having a wavelength of 0.1659 nm is used, compute (a) the interplanar spacing for this set of planes, and (b) the atomic radius for the niobium atom.

Solution: From the data given in the problem, and realizing that 75.99° = 2θ, the interplanar spacing for the (211) set of planes for Nb may be computed using the following Equation:

In order to compute the atomic radius we must first determine the lattice parameter, a, and then R since Nb has a BCC crystal structure. Therefore,

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12. The results of a diffraction experiment using X-Rays with λ = 0.7107 Å (radiation obtained from a molybdenum, Mo, target) show that diffracted peaks occur at the following 2θ angles:

Find the interplanar spacing (d-spacing) and the lattice parameter (a) of the material?

13. How much should be the energy of X-ray to generate wavelength of 10-10m, (h= 4.1357 × 10-15 eV.s, and c=3×108m)

14. Determine on the following diagram: 1) X-ray wavelength, 2) d spacing, 3) Angle of incident, 4) Angle of reflection. 5) Atomic plane.

15. Construct a Primitive Cell for the following lattice using the Wigner-Seitz Method

16. Derive Ohm’s law using Drude theory? We apply an electric field. The equation of motion is:

Integration gives:

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Number of electrons passing in unit time:

Current density

Ohm's law:

17. If the following figure represents a 2 dimensional (2D) lattice crystal, answer the following questions Draw 2 possible primitive unit cells. Draw other 2 possible conventional unit cells. Show 2 possible primitive lattice vectors.

18. Here is the energy diagram against the interatomic separation between two atoms. Where on the x-axis, the Cl atom have the most stable position regarding to the positive Na atom on point zero?

19. Discuss the monoatomic chain model and show the ω versus k relation as a mathematical equation and a graph.

20. Explain the X-Ray Production, how the wavelength of these radiation can be controlled?

21. Use your knowledge of chemical bonding and the following electronegativity table to arrange the bonds in order of increasing ionic character in the molecules: LiF, K2O, N2, NaCl and ClF3 :

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Electronegativity table

22. Q5: The following figure shows the Germanium Energy Bands. Determine the energy gap, if it exists, on the Figure and explain briefly the electrical properties of this element?

23. The following figure shows the lattice points of a crystal, classify the 6 shown cells according to the table below:

Type of cell Cell #Primitive unit cellNon-primitive unit cellNot a unit cell

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Construct on the previous figure a primitive unit cell using Wigner-Seitz Method 24. Discuss briefly Heat Capacity using the classical Model and Einstein Model.25. The following Figure shows the BCC structure, determine the lattice points of atoms

with numbers 1, 2, 3 and 8

26. Express or define in less than one line the following

Dispersion relations: Bragg law: The vibration in a Monoatomic Chain (graph)?

27. Explain the Wiedemann-Franz law.28. Discuss briefly the generation of X-rays 29. Discuss the chemical bonding of SiC (see the Electronegativity table)

30. For BCC iron, compute (a) the interplanar spacing, and (b) the diffraction angle for the (220) set of planes. The lattice parameter for Fe is 0.2866 nm. Also, assume that monochromatic radiation having a wavelength of 0.1790 nm is used, and the order of reflection is 1.

Solution:

(a) The value of the interplanar spacing is determined, with a= 0.2866 nm, and h= 2, k = 2, l = 0, and since we are considering the (220) planes. Therefore,

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(b) The value of ɵ may now be computed, with n=1 since this is a first-order reflection:

The diffraction angle is 2ɵ or:

31. The metal rhodium has an FCC crystal structure. If the angle of diffraction for the (311) set of planes occurs at 36.12o (first-order reflection) when monochromatic x-radiation having a wavelength of 0.0711 nm is used, compute (a) the interplanar spacing for this set of planes, and (b) the atomic radius for a rhodium atom.

Solution:

(a) From the data given in the problem, and realizing that 36.12° = 2θ, the interplanar spacing for the (311) set of planes for rhodium may be computed using the following Equation:

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(b) In order to compute the atomic radius we must first determine the lattice parameter, a, and then R , since Rh has an FCC crystal structure. Therefore,

32. The metal niobium has a BCC crystal structure. If the angle of diffraction for the (211) set of planes occurs at 75.99o (first-order reflection) when monochromatic x-radiation having a wavelength of 0.1659 nm is used, compute (a) the interplanar spacing for this set of planes, and (b) the atomic radius for the niobium atom.

Solution:

(a) From the data given in the problem, and realizing that 75.99° = 2θ, the interplanar spacing for the (211) set of planes for Nb may be computed using the following Equation:

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(b) In order to compute the atomic radius we must first determine the lattice parameter, a, and then R since Nb has a BCC crystal structure. Therefore,

33. What is the magnitude of the force required to stretch a 20 cm-long spring, with a spring constant of 100 N/m, to a length of 21 cm? 

The spring changes from a length of 20 cm to 21 cm, hence it stretches by 1 cm or |Δx  | = 1 cm = 0.01 m. | F | = k | Δx  | = 100 N / m × 0.01 m = 1 N

1. If the unit cell has 3 atoms, thus how many phonon modes are present

3N modes. Therefore 9 modes.

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34. If the velocity of sound in a solid is taken to be 3 x 103m/s and interatomic distance as 5 x 10-10 m, calculate the value of cutoff frequency assuming a linear lattice.

Velocity of sound in a solid (v) is 3 x 103m/s Interatomic distance (a) is 5 x 10-10 m

Velocity and frequency related equation:

Apply the known values in the equation. Critical frequency (w) = 3× 1012 HZ

35. Below is a displacement-time graph of a wave. (Displacement) in meters is on the y-axis and time in seconds is on the x-axis. Determine: (a) the amplitude of the wave (b) the period of the wave (c) the frequency of the wave

2.2 m 4 s 0.25

36. A wave on a rope is shown below. (a) What is the wavelength of this wave? (b) If the frequency of this wave is 4 Hz, what is its

3m 12m/s

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37. 6. If the velocity of sound in a solid is of the order 10 3 m/s, compare the frequency of the sound wave λ = 20 Å for (a) a monoatomic system and (b) acoustic waves and optical waves in a diatomic system containing two identical atoms (M=m) per unit cell of interatomic spacing 2.2 Å.

o Given value:

Velocity of sound in a solid = 103 m/s Sound wave λ = 20 x 10-10 m Interatomic spacing (a) = 2.2 ×10-10 m

I. In case of homogenous line, the frequency :

II. a. Acoustic wave in a diatomic ( identical M=m) lattice, the frequency varies from

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b. Optical wave, the frequency varies from:

38.

The unit cell parameter of NaCl is 5.65Å and the modulus of elasticity along [100] direction is 6 x 1010 N/m2. Estimate the wavelength at which an electromagnetic radiation is strongly reflected by the crystal. At. Wt. of Na = 23 and of Cl = 37

o Given value:

Unit cell parameter (a) = 5.65 x 10-10 m Modulus of elasticity (Y) = 6 x 1010 N/m2

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The maximum frequency of radiation strongly reflected by the NaCl crystal will be given by:

Let us assume that an extension along [100] direction will have negligible effect on vertical springs. Therefore, we can write:

The frequency expression becomes

where M and m be the atomic weight of the crystal, and considered the atomic mass unit.

Atomic weight of chlorine (M) = 37 Atomic weight of sodium (m) = 23 Atomic mass unit = 1.67 × 10-27 Kg

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Hence the wavelength at which this radiation is strongly reflected is

where ω = 5.13×1013 rad/sec, c is the velocity of light then,

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