FSc Pre-Engineering Physics Physics of Solids — Set 2

FSc Pre-Engineering Physics Physics of Solids — Set 2

1. Question 1

   Q1. What is the typical crystal structure of NaCl?

   • A) Face-Centered Cubic (FCC)
   • B) Body-Centered Cubic (BCC)
   • C) Hexagonal Close-Packed (HCP)
   • D) Diamond Cubic

   Answer: Face-Centered Cubic (FCC)

   Explanation: NaCl has a face-centered cubic lattice with a basis of two atoms, Na and Cl, at (0,0,0) and (1/2, 1/2, 1/2).

2. Question 2

   Q2. The energy gap in a semiconductor is 1.1 eV. What is the maximum wavelength of light that can be absorbed?

   • A) 1.12 μm
   • B) 1.13 μm
   • C) 1.14 μm
   • D) 1.15 μm

   Answer: 1.13 μm

   Explanation: Using E = hc / λ, we get λ = hc / E = (6.626 × 10^-34 × 3 × 10^8) / (1.1 × 1.6 × 10^-19) = 1.13 μm.

3. Question 3

   Q3. A metal has a density of 8.9 g/cm³ and atomic weight 63.5 g/mol. If it has a FCC structure, what is the lattice parameter?

   • A) 3.6 Å
   • B) 3.7 Å
   • C) 3.8 Å
   • D) 3.9 Å

   Answer: 3.6 Å

   Explanation: Using the formula ρ = nM / (N_A a³), we can find a = (nM / (N_A ρ))^(1/3) = 3.6 Å for n = 4 in FCC.

4. Question 4

   Q4. The reciprocal of the Hall coefficient gives?

   • A) Carrier concentration
   • B) Mobility
   • C) Conductivity
   • D) Resistivity

   Answer: Carrier concentration

   Explanation: RH = 1 / ne, so 1 / RH = ne, which is the carrier concentration.

5. Question 5

   Q5. The Miller indices of a plane are (1 1 1). What is the intercept on the z-axis?

   • A) 1
   • B) 1/2
   • C) 1/3
   • D) 1/1

   Answer: 1

   Explanation: For (1 1 1), the intercepts are 1, 1, 1 on the x, y, and z axes, respectively.

6. Question 6

   Q6. The ratio of the specific heat capacities at constant pressure and constant volume for a monatomic gas is?

   • A) 5/3
   • B) 3/5
   • C) 7/5
   • D) 5/7

   Answer: 5/3

   Explanation: For a monatomic gas, Cp / Cv = (5/2 R) / (3/2 R) = 5/3.

7. Question 7

   Q7. A semiconductor has a bandgap of 0.7 eV. At what temperature will the intrinsic carrier concentration be 10^16 cm^-3?

   • A) 300 K
   • B) 400 K
   • C) 500 K
   • D) 600 K

   Answer: 500 K

   Explanation: Using ni = √(Nc Nv) exp(-Eg / 2kT), we can find T = Eg / (2k ln(√(Nc Nv) / ni)) = 500 K.

8. Question 8

   Q8. What is the coordination number of a BCC lattice?

   • A) 8
   • B) 6
   • C) 12
   • D) 4

   Answer: 8

   Explanation: In a BCC lattice, each atom is surrounded by 8 nearest neighbors.

9. Question 9

   Q9. The drift velocity is directly proportional to?

   • A) Electric field
   • B) Magnetic field
   • C) Temperature
   • D) Carrier concentration

   Answer: Electric field

   Explanation: vd = μE, where μ is the mobility and E is the electric field.

10. Question 10

    Q10. The Bragg's law is given by?

    • A) 2d sinθ = nλ
    • B) d sinθ = nλ
    • C) 2d cosθ = nλ
    • D) d cosθ = nλ

    Answer: 2d sinθ = nλ

    Explanation: Bragg's law states that 2d sinθ = nλ, where d is the interplanar spacing and θ is the angle of incidence.

11. Question 11

    Q11. The density of states in a 3D system is proportional to?

    • A) E^(1/2)
    • B) E
    • C) E^(3/2)
    • D) E²

    Answer: E^(1/2)

    Explanation: The density of states in 3D is given by g(E) ∝ E^(1/2).

12. Question 12

    Q12. The Fermi energy is the energy of?

    • A) The highest occupied state at T = 0 K
    • B) The lowest unoccupied state at T = 0 K
    • C) The average energy of electrons
    • D) The energy of the conduction band edge

    Answer: The highest occupied state at T = 0 K

    Explanation: At T = 0 K, all states below EF are filled, making EF the energy of the highest occupied state.

13. Question 13

    Q13. The type of bonding in NaCl is?

    • A) Ionic
    • B) Covalent
    • C) Metallic
    • D) Van der Waals

    Answer: Ionic

    Explanation: NaCl is a classic example of ionic bonding due to the large electronegativity difference between Na and Cl.

14. Question 14

    Q14. The critical temperature of a superconductor is the temperature below which?

    • A) The material becomes resistive
    • B) The material becomes superconducting
    • C) The material becomes ferromagnetic
    • D) The material becomes antiferromagnetic

    Answer: The material becomes superconducting

    Explanation: Below Tc, a superconductor exhibits zero resistance and perfect diamagnetism.

15. Question 15

    Q15. What is the packing efficiency of face-centered cubic (FCC) lattice?

    • A) 74%
    • B) 68%
    • C) 52%
    • D) 90%

    Answer: 74%

    Explanation: FCC has 4 atoms per unit cell. Packing efficiency = (4 * (4/3) * π * r³) / a³, where a = 2√2r. Simplifying gives 74%.

16. Question 16

    Q16. The dispersion relation for phonons in a one-dimensional lattice is ω = ±√(4K/M) |sin(πk/2)|. What is the maximum frequency?

    • A) √(4K/M)
    • B) √(2K/M)
    • C) 2√(K/M)
    • D) √(K/M)

    Answer: √(4K/M)

    Explanation: Maximum frequency occurs when sin(πk/2) = 1, so ω_max = √(4K/M).

17. Question 17

    Q17. In a ferromagnetic material, the Curie temperature is 500 K. At 300 K, the susceptibility is 10^(-3). What is the susceptibility at 400 K?

    • A) 2 * 10^(-3)
    • B) 5 * 10^(-4)
    • C) 1.25 * 10^(-3)
    • D) 8 * 10^(-4)

    Answer: 1.25 * 10^(-3)

    Explanation: Using Curie's law, χ = C / (T - T_c), and given χ at 300 K, we can find C and then χ at 400 K.

18. Question 18

    Q18. The Fermi energy of a metal is 5 eV. What is the average energy of electrons at 0 K?

    • A) 2.5 eV
    • B) 3 eV
    • C) 3.75 eV
    • D) 5 eV

    Answer: 3.75 eV

    Explanation: Average energy = (3/5) * E_f = (3/5) * 5 eV = 3 eV. However, for a more precise calculation, it's (3/5) * E_f for a non-interacting Fermi gas.

19. Question 19

    Q19. A superconductor has a critical temperature of 4 K. At 2 K, the critical magnetic field is 10^(-2) T. What is the critical field at 0 K?

    • A) 1.33 * 10^(-2) T
    • B) 1.25 * 10^(-2) T
    • C) 1.5 * 10^(-2) T
    • D) 2 * 10^(-2) T

    Answer: 1.33 * 10^(-2) T

    Explanation: Using the relation H_c(T) = H_c(0) * [1 - (T/T_c)²], we can find H_c(0).

20. Question 20

    Q20. The density of states for a two-dimensional electron gas is proportional to

    • A) √E
    • B) E
    • C) 1
    • D) 1/√E

    Answer: 1

    Explanation: For 2D, the density of states is constant and does not depend on energy.