Nanoworld Quiz

1. What is the form of the ground state wavefunction \( \psi_1(x) \) for a particle in a 1D infinite potential well of width \( L \)?

(A) \( \psi_1(x) = \cos\left(\frac{\pi x}{L}\right) \)
(B) \( \psi_1(x) = \sqrt{\frac{2}{L}} \sin\left(\frac{\pi x}{L}\right) \)
(C) \( \psi_1(x) = \sqrt{\frac{1}{L}} \sin\left(\frac{2\pi x}{L}\right) \)
(D) \( \psi_1(x) = \sqrt{\frac{2}{L}} \cos\left(\frac{\pi x}{L}\right) \)

2. The energy levels of a particle confined in a 1D infinite potential well of width \( L \) are given by:

(A) \( E_n = \frac{n^2 \hbar^2}{mL^2} \)
(B) \( E_n = \frac{n^2 \pi^2 \hbar^2}{2mL^2} \)
(C) \( E_n = \frac{n \hbar}{2L} \)
(D) \( E_n = \frac{n \pi \hbar}{mL} \)

3. What is the wavelength of the nth eigenfunction in a 1D infinite potential well of width \( L \)?

(A) \( \lambda_n = 2L/n^2 \)
(B) \( \lambda_n = L/n \)
(C) \( \lambda_n = 2L/n \)
(D) \( \lambda_n = 4L/n \)

4. In the region outside a finite potential well (where \( E < V_0 \)), the wavefunction:

(A) Oscillates with constant amplitude
(B) Becomes zero
(C) Decays exponentially
(D) Grows exponentially

5. What physical phenomenon allows a particle to exist in a classically forbidden region?

(A) Classical leakage
(B) Quantum tunneling
(C) Thermal fluctuation
(D) Resonance

6. The transmission probability \( T \) for a particle of energy \( E < V_0 \) through a barrier of width \( a \) is approximately:

(A) \( T \approx e^{ka} \)
(B) \( T \approx a^2 \)
(C) \( T \approx e^{-2ka} \)
(D) \( T \approx \frac{1}{ka} \)

7. What does the parameter \( k \) in the tunneling formula \( T \approx e^{-2ka} \) represent?

(A) Momentum of the particle
(B) Energy of the particle
(C) Decay constant: \( k = \sqrt{\frac{2m(V_0 - E)}{\hbar^2}} \)
(D) Wavelength inside the barrier

8. Which of the following correctly describes a bound state in a finite potential well?

(A) Energy \( E \ge V_0 \)
(B) Particle is free to escape
(C) Energy \( E < V_0 \), wavefunction decays outside well
(D) Wavefunction is constant throughout

9. For a particle in a 1D box, the probability of finding it at the center \( x = L/2 \) in the first excited state is:

(A) Maximum
(B) Zero
(C) Minimum but non-zero
(D) Always 1

10. Nil

(A) Option A
(B) Option B
(C) Option C
(D) Option D

11. Which of the following best describes a quantum dot?

(A) A 1D nanostructure with length but no confinement in other directions
(B) A periodic layer of two different materials
(C) A thin conducting layer confined in one direction
(D) A 0D structure with confinement in all three spatial dimensions

12. In a quantum dot, the energy levels are quantized due to:

(A) Phonon interactions
(B) Spatial confinement of electrons in all directions
(C) External electric field
(D) Magnetic coupling

13. Which structure has confinement in two spatial directions?

(A) Nanowire
(B) Quantum well
(C) Quantum dot
(D) Bulk crystal

14. The energy spacing in a quantum dot is approximately given by:

(A) \( \Delta E \propto \frac{1}{L^2} \)
(B) \( \Delta E \propto L \)
(C) \( \Delta E \propto \ln(L) \)
(D) \( \Delta E \propto \sqrt{L} \)

15. A nanowire behaves as a one-dimensional system because:

(A) Its length is atomic scale
(B) It allows free motion along one axis with confinement in other two
(C) All electrons are localized
(D) Electrons have zero effective mass

16. What is a superlattice?

(A) A single material structure with quantum confinement
(B) A crystal formed by isotropic atoms
(C) A periodic structure of alternating thin layers of different semiconductors
(D) A doped quantum dot

17. In heterostructures, band alignment is important because:

(A) It determines carrier confinement and transport properties
(B) It ensures isotropic bonding
(C) It prevents electron tunneling
(D) It suppresses phonons

18. The primary reason quantum confinement occurs in nanostructures is:

(A) Surface tension
(B) Thermal motion
(C) Restriction of electron motion due to dimensions comparable to de Broglie wavelength
(D) Electric field at boundary

19. If a quantum dot radius is halved, the energy level spacing:

(A) Halves
(B) Quadruples
(C) Doubles
(D) Remains constant

20. Which of the following materials systems is typically used in quantum well heterostructures?

(A) GaAs/AlGaAs
(B) Si/Cu
(C) Ag/Au
(D) Fe/Co

21. Which technique is commonly used for the top-down fabrication of quantum nanostructures?

(A) Sol-gel synthesis
(B) Chemical vapor deposition
(C) Self-assembly
(D) Electron beam lithography

22. In quantum nanostructures, the effect of reduced dimensionality leads to:

(A) Increase in density of states
(B) Quantization of energy levels
(C) Increase in thermal conductivity
(D) Linear band structure

23. What phenomenon allows electrons to tunnel one-by-one through a nanoscale junction?

(A) Coulomb explosion
(B) Single electron tunneling
(C) Ballistic transport
(D) Quantum Hall effect

24. A necessary condition for observing single-electron tunneling is:

(A) Low capacitance and high resistance junction
(B) Capacitance such that charging energy exceeds thermal energy
(C) High tunneling rate
(D) Degenerate energy levels

25. Metal nanoclusters are often characterized by:

(A) Discrete electronic energy levels
(B) Continuous band structures
(C) Lack of optical properties
(D) Bulk metallic behavior

26. Semiconducting nanoparticles exhibit size-dependent color because:

(A) Electron spin splitting
(B) Magnetic coupling
(C) Band gap increases as particle size decreases
(D) Surface defects emit white light

27. Rare gas clusters are held together primarily by:

(A) van der Waals interactions
(B) Covalent bonds
(C) Ionic bonding
(D) Metallic bonds

28. Which of the following is a common method to create self-assembled nanostructures?

(A) Ball milling
(B) Langmuir-Blodgett technique
(C) Arc discharge
(D) Laser ablation

29. In catalytic applications, nanoparticles are preferred due to:

(A) High thermal conductivity
(B) High melting point
(C) Large surface area to volume ratio
(D) Strong covalent bonds

30. Which of the following is true about molecular clusters?

(A) They have purely metallic properties
(B) Their properties do not vary with size
(C) Their electronic and optical properties depend on the number of atoms
(D) They are stable only in plasma

31. What does the quantum leak or tunneling in nanostructures primarily depend on?

(A) Electron temperature
(B) Width and height of the potential barrier
(C) Crystal defects
(D) Magnetic field strength

32. Which of the following nanostructures has confinement in only one direction?

(A) Quantum dot
(B) Quantum well
(C) Nanowire
(D) Superlattice

33. In a superlattice, the periodicity arises from:

(A) Alternating layers of different materials
(B) Atomic doping
(C) Defect positioning
(D) Isolated impurities

34. What is the key parameter that governs quantum confinement effects in nanoparticles?

(A) Lattice constant
(B) Particle size relative to de Broglie wavelength
(C) Electron affinity
(D) Crystal symmetry

35. Which synthesis method is a bottom-up physical deposition technique?

(A) Molecular Beam Epitaxy (MBE)
(B) Nanolithography
(C) Mechanical alloying
(D) Ball milling

36. Which method is a top-down approach for synthesizing nanostructures?

(A) Chemical vapor deposition (CVD)
(B) Pulsed laser deposition (PLD)
(C) Nanolithography
(D) Self-assembly

37. What characterizes single electron tunneling in nanostructures?

(A) Discrete transfer of electrons due to Coulomb blockade
(B) Rapid electron avalanching
(C) Suppressed band gap
(D) Thermionic emission

38. Which of the following structures shows discrete molecular-like energy states?

(A) Metal nanoclusters
(B) Bulk semiconductors
(C) Crystalline polymers
(D) Nanotubes

39. Which method is commonly used for wet chemical synthesis of nanoparticles?

(A) Sol-gel method
(B) Ion implantation
(C) Laser ablation
(D) Sputtering

40. In catalysis, why is self-assembly advantageous in nanoparticle synthesis?

(A) It reduces surface defects
(B) It allows formation of ordered nanostructures with high surface area
(C) It minimizes the use of solvents
(D) It increases conductivity of nanoparticles

41. What is the crystal structure of monolayer graphene?

(A) Square lattice of carbon atoms
(B) Two-dimensional hexagonal honeycomb lattice
(C) Body-centered cubic structure
(D) Tetragonal lattice with sp³ hybridization

42. What distinguishes superparamagnetic nanoparticles from ferromagnetic ones?

(A) They exhibit permanent magnetization without a field
(B) They are always diamagnetic
(C) They have zero remanent magnetization due to thermal fluctuations
(D) Their magnetization increases with temperature

43. Superparamagnetic behavior is typically observed when:

(A) Particle size exceeds 100 nm
(B) Particle size is below a critical size, typically < 10 nm
(C) Particles are in clusters
(D) Magnetic domains are fixed

44. In Giant Magnetoresistance (GMR), the resistance change is due to:

(A) Thermionic emission
(B) Electron tunneling through vacuum
(C) Spin-dependent scattering in multilayers
(D) Lattice distortion

45. Which structure is key in GMR devices?

(A) Graphene monolayer
(B) Nanopillars
(C) Alternating ferromagnetic and nonmagnetic layers
(D) Metal-oxide heterojunction

46. What is a key application of ferrofluids?

(A) Damping and sealing in rotating shafts
(B) Lubrication of solar panels
(C) Electroluminescence
(D) DNA sequencing

47. A characteristic feature of ferrofluids is:

(A) Magnetic ordering at room temperature
(B) Strong response to external magnetic field without aggregation
(C) Permanent magnetization in zero field
(D) Conductivity enhancement

48. Colossal magnetoresistance (CMR) is most commonly observed in:

(A) Nickel-based alloys
(B) Perovskite manganites
(C) Silicon wafers
(D) Metal-graphene composites

49. CMR materials exhibit a change in resistance due to:

(A) Magnetic field-induced transition from insulating to metallic phase
(B) Photoexcitation
(C) Quantum confinement
(D) Lattice strain alone

50. Nanostructured thermal devices can enhance heat transfer due to:

(A) Increased photon emission
(B) Increased surface area and phonon scattering
(C) Reduced thermal conductivity of substrate
(D) Enhanced magnetism

51. Which of the following is NOT a characteristic of superhydrophobic nanostructured surfaces?

(A) Contact angle greater than 150°
(B) Low contact angle hysteresis
(C) Strong adhesion to water droplets
(D) Surface roughness at nano/micro scale

52. The "lotus effect" is associated with:

(A) Surface plasmon resonance
(B) Superhydrophobicity due to hierarchical structures
(C) Magnetic ordering in biological systems
(D) Optical birefringence

53. A key strategy in biomimetics is to:

(A) Mimic physical behavior of noble gases
(B) Enhance friction of materials
(C) Design materials based on biological forms and processes
(D) Replace carbon with nitrogen atoms

54. Which biomimetic nanostructure has inspired gecko-inspired adhesives?

(A) Spider silk structure
(B) Hierarchical setae on gecko foot
(C) Honeycomb cell walls
(D) Sharkskin ridges

55. Which of the following is a potential use of biomimetic nanostructures?

(A) Anti-reflective coatings inspired by moth eyes
(B) Purely decorative coatings
(C) Energy storage by osmosis
(D) Radio wave generation

Student Details

Quiz: Applications of Schrödinger Equation in the Nanoworld