UET Lahore ECAT Physics: Physics of Solids MCQs

UET Lahore ECAT Physics: Physics of Solids MCQs — sample questions

1. Question 1

   Q1. What is the energy of a photon emitted when an electron jumps from n = 3 to n = 2 in a hydrogen atom?

   • A) 1.89 eV
   • B) 2.55 eV
   • C) 1.51 eV
   • D) 3.4 eV

   Answer: 1.89 eV

   Explanation: Energy of photon = 13.6 (1/2² - 1/3²) = 13.6 (1/4 - 1/9) = 1.89 eV, using Bohr's model energy level formula.

2. Question 2

   Q2. The ratio of the radius of the second orbit of He+ to that of the third orbit of Be3+ is

   • A) 3/8
   • B) 2/9
   • C) 1/3
   • D) 9/2

   Answer: 2/9

   Explanation: Radius ∝ n²/Z; ratio = (2²/2)/(3²/4) = 2/9, applying the formula for radius of nth orbit in hydrogen-like atoms.

3. Question 3

   Q3. In a p-type semiconductor, the acceptor level lies

   • A) just below the valence band
   • B) just above the valence band
   • C) in the middle of the band gap
   • D) just above the conduction band

   Answer: just below the valence band

   Explanation: In p-type, acceptor level is near valence band, allowing easy acceptance of electrons, thus creating holes, using the concept of doping in semiconductors.

4. Question 4

   Q4. The effective mass of an electron in a crystal is

   • A) always positive
   • B) always negative
   • C) sometimes negative
   • D) zero

   Answer: sometimes negative

   Explanation: Effective mass can be negative near the top of the band due to the curvature of E-k diagram, a concept from solid-state physics.

5. Question 5

   Q5. The Hall coefficient is given by

   • A) 1/ne
   • B) ne
   • C) -1/ne
   • D) 1/n²e

   Answer: 1/ne

   Explanation: Hall coefficient = 1/ne, derived from the Hall effect equation, relating carrier concentration and Hall voltage.

6. Question 6

   Q6. The Fermi level in an intrinsic semiconductor lies

   • A) at the bottom of the conduction band
   • B) at the top of the valence band
   • C) in the middle of the band gap
   • D) within the valence band

   Answer: in the middle of the band gap

   Explanation: In intrinsic semiconductors, the Fermi level is at the center of the band gap due to equal probability of electron and hole creation.

7. Question 7

   Q7. The density of states in a 3D solid is proportional to

   • A) E
   • B) √E
   • C) E²
   • D) 1/√E

   Answer: √E

   Explanation: Density of states ∝ √E, derived from the 3D density of states formula, g(E) = (√2 m³/2 π² ħ³) √E.

8. Question 8

   Q8. A crystal has a lattice parameter of 4 Å. The d-spacing between (1 1 1) planes is

   • A) 2.31 Å
   • B) 4.0 Å
   • C) 2.0 Å
   • D) 1.15 Å

   Answer: 2.31 Å

   Explanation: d = a / √(h² + k² + l²) = 4 / √3 = 2.31 Å, using the formula for interplanar spacing in a cubic lattice.

9. Question 9

   Q9. The Wiedemann-Franz law relates

   • A) thermal conductivity and electrical conductivity
   • B) thermal conductivity and Seebeck coefficient
   • C) electrical conductivity and Seebeck coefficient
   • D) none of the above

   Answer: thermal conductivity and electrical conductivity

   Explanation: Wiedemann-Franz law states that K/σ = LT, relating thermal and electrical conductivity, a fundamental concept in solid-state physics.

10. Question 10

    Q10. The reciprocal lattice vector is

    • A) perpendicular to the lattice plane
    • B) parallel to the lattice plane
    • C) perpendicular to the real lattice vector
    • D) parallel to the real lattice vector

    Answer: perpendicular to the lattice plane

    Explanation: Reciprocal lattice vector is normal to the lattice plane, a property derived from the definition of reciprocal lattice.

11. Question 11

    Q11. In a ferromagnetic material, the Curie temperature is

    • A) the temperature below which it is ferromagnetic
    • B) the temperature above which it is ferromagnetic
    • C) the temperature at which it becomes paramagnetic
    • D) both A and C

    Answer: both A and C

    Explanation: Curie temperature is the threshold below which a material is ferromagnetic and above which it becomes paramagnetic.

12. Question 12

    Q12. The London penetration depth is related to

    • A) superconductivity
    • B) semiconductivity
    • C) ferromagnetism
    • D) paramagnetism

    Answer: superconductivity

    Explanation: London penetration depth is a measure of the depth to which a magnetic field penetrates a superconductor, related to Meissner effect.

13. Question 13

    Q13. The energy gap in a semiconductor is 1 eV. The wavelength of the emitted radiation when an electron recombines with a hole is

    • A) 1240 nm
    • B) 620 nm
    • C) 2480 nm
    • D) 310 nm

    Answer: 1240 nm

    Explanation: λ = hc/E = (6.626 × 10^-34 × 3 × 10^8) / (1.6 × 10^-19 × 1) = 1240 nm, using the formula for energy of a photon.

14. Question 14

    Q14. The Miller indices of a plane are (1 1 0). The intercepts on the x, y, and z axes are

    • A) 1, 1, ∞
    • B) 1, 1, 0
    • C) 1, -1, ∞
    • D) 1, 1, 1

    Answer: 1, 1, ∞

    Explanation: Miller indices (1 1 0) imply intercepts 1, 1, ∞ on x, y, z axes respectively, using the definition of Miller indices.

15. Question 15

    Q15. The type of bonding in NaCl crystal is

    • A) ionic
    • B) covalent
    • C) metallic
    • D) van der Waals

    Answer: ionic

    Explanation: NaCl is an example of ionic bonding, where electrons are transferred between atoms, resulting in electrostatic attraction.

16. Question 16

    Q16. The electrical conductivity of a metal decreases with increasing temperature because

    • A) the number of electrons increases
    • B) the number of electrons decreases
    • C) the electron-phonon interaction increases
    • D) the electron-phonon interaction decreases

    Answer: the electron-phonon interaction increases

    Explanation: Increased temperature enhances electron-phonon interaction, reducing conductivity, a concept from the study of electrical conductivity in metals.

17. Question 17

    Q17. The phenomenon of superconductivity was discovered by

    • A) Heike Kamerlingh Onnes
    • B) Pierre Curie
    • C) Marie Curie
    • D) Albert Einstein

    Answer: Heike Kamerlingh Onnes

    Explanation: Heike Kamerlingh Onnes discovered superconductivity in 1911, observing zero resistance in mercury at very low temperatures.

18. Question 18

    Q18. The Debye temperature is a measure of

    • A) the maximum frequency of vibration
    • B) the minimum frequency of vibration
    • C) the average frequency of vibration
    • D) none of the above

    Answer: the maximum frequency of vibration

    Explanation: Debye temperature is related to the maximum frequency of lattice vibrations, a concept from the Debye model of specific heat.

19. Question 19

    Q19. The Meissner effect is a characteristic of

    • A) superconductors
    • B) semiconductors
    • C) ferromagnets
    • D) paramagnets

    Answer: superconductors

    Explanation: Meissner effect, the expulsion of magnetic fields from a superconductor, is a defining property of superconducting materials.

20. Question 20

    Q20. The BCS theory explains

    • A) superconductivity
    • B) superfluidity
    • C) ferromagnetism
    • D) paramagnetism

    Answer: superconductivity

    Explanation: BCS theory, proposed by Bardeen, Cooper, and Schrieffer, explains the phenomenon of superconductivity through Cooper pairs.