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Quantum tunnelling - Quiz
Contributed by: Gregory
  • 1. In what year was the Schrödinger equation published?
A) 1925
B) 1926
C) 1928
D) 1927
  • 2. Who was the first person to apply the Schrödinger equation to a problem involving tunnelling?
A) George Gamow
B) Leonid Mandelstam
C) Friedrich Hund
D) Erwin Schrödinger
  • 3. What physical system did Friedrich Hund study while investigating tunnelling in 1927?
A) An infinite potential well
B) A double-well potential
C) A semiconductor diode
D) A single-well potential
  • 4. Who discovered tunnelling independently alongside Mikhail Leontovich and published their results in 1928?
A) Lothar Nordheim
B) Ralph Fowler
C) Leonid Mandelstam
D) Yakov Frenkel
  • 5. Who assisted Lothar Nordheim in publishing a paper discussing thermionic emission in 1927?
A) J. Robert Oppenheimer
B) Ralph Fowler
C) Brian Josephson
D) Walter Schottky
  • 6. What did Lothar Nordheim's 1927 paper discuss?
A) Thermionic emission and reflection of electrons from metals
B) Superconducting energy gaps
C) Scanning tunnelling microscopy
D) Alpha decay half-lives
  • 7. According to classical physics, what is the probability that an electron transmits or reflects at a surface barrier?
A) 100%
B) 0%
C) 50%
D) Variable
  • 8. In what year did J. Robert Oppenheimer publish two papers on field emission?
A) 1931
B) 1926
C) 1927
D) 1928
  • 9. What phenomenon did J. Robert Oppenheimer study in his 1928 papers?
A) Field emission
B) Alpha decay
C) Superconductivity
D) Thermionic emission
  • 10. Who provided a mathematical explanation for alpha decay in 1928?
A) Lothar Nordheim and Ralph Fowler
B) Friedrich Hund and Leonid Mandelstam
C) Leo Esaki and Ivar Giaever
D) George Gamow, Ronald Gurney, and Edward Condon
  • 11. What relationship did Gurney and Condon derive when solving the Schrödinger equation for a model nuclear potential?
A) Between temperature and electrical resistance
B) Between the half-life of the particle and the energy of emission
C) Between barrier width and current voltage
D) Between magnetic field and superconductivity
  • 12. What German term for the tunnel effect was used by Walter Schottky in 1931?
A) Tunneleffekt
B) Wellenmechanischer Tunneleffekt
C) Tunnelierung
D) Quantenbarriere
  • 13. Who introduced the English term 'tunnel effect' in a textbook in 1932?
A) Walter Schottky
B) George Gamow
C) Lothar Nordheim
D) Yakov Frenkel
  • 14. What were early quantum theorists referring to when they described the tunnel effect?
A) Penetration of, or leaking through, a barrier
B) Wave-particle duality
C) Atomic imaging
D) Reflection of electrons from metals
  • 15. Who demonstrated the tunnelling of electrons across a few nanometre wide barrier in a semiconductor structure in 1957?
A) Brian Josephson
B) Gerd Binnig
C) Ivar Giaever
D) Leo Esaki
  • 16. What type of device did Leo Esaki develop based on the tunnel effect?
A) A scanning tunnelling microscope
B) A diode
C) A superconductor circuit
D) A thermionic emitter
  • 17. Who showed experimentally that tunnelling also took place in superconductors in 1960?
A) Brian Josephson
B) Heinrich Rohrer
C) Leo Esaki
D) Ivar Giaever
  • 18. What direct evidence did the tunnelling spectrum provide in Ivar Giaever's 1960 experiments?
A) Macroscopic quantum states
B) Atomic resolution images
C) The superconducting energy gap
D) The half-life of alpha particles
  • 19. Who predicted the tunnelling of superconducting Cooper pairs in 1962?
A) Brian Josephson
B) Ivar Giaever
C) John Clarke
D) Leo Esaki
  • 20. Which scientists shared the 1973 Nobel Prize in Physics for their works on quantum tunnelling in solids?
A) Clarke, Martinis, and Devoret
B) Gamow, Gurney, and Condon
C) Esaki, Giaever, and Josephson
D) Binnig, Rohrer, and Esaki
  • 21. Who developed the scanning tunnelling microscope in 1981?
A) Friedrich Hund and Walter Schottky
B) Leo Esaki and Ivar Giaever
C) John Clarke and John M. Martinis
D) Gerd Binnig and Heinrich Rohrer
  • 22. What is the primary use of a scanning tunnelling microscope?
A) Detecting alpha decay half-lives
B) Observing macroscopic quantum circuits
C) Imaging surfaces at the atomic level
D) Measuring semiconductor diode resistance
  • 23. In what year were Gerd Binnig and Heinrich Rohrer awarded the Nobel Prize in Physics for their microscope discovery?
A) 1973
B) 1986
C) 2025
D) 1981
  • 24. Which scientists received the 2025 Nobel Prize in Physics for demonstrating quantum tunnelling on a macroscopic scale?
A) George Gamow, Ronald Gurney, and Edward Condon
B) Gerd Binnig, Heinrich Rohrer, and Brian Josephson
C) Leo Esaki, Ivar Giaever, and Lothar Nordheim
D) John Clarke, John M. Martinis, and Michel H. Devoret
  • 25. In which years were the experiments by Clarke, Martinis, and Devoret on macroscopic quantum tunnelling conducted?
A) 1981 and 1986
B) 1957 and 1960
C) 1927 and 1928
D) 1984 and 1985
  • 26. What components did Clarke, Martinis, and Devoret use in their electrical circuit to demonstrate macroscopic tunnelling?
A) Two superconductors separated by a thin non-conducting layer of material
B) A double-well potential and an electron emitter
C) Two semiconductor diodes separated by a nanometre barrier
D) A scanning tip and an atomic surface
  • 27. In the macroscopic tunnelling experiments, how did the charged particles in the superconductor behave?
A) Individually with a 100% reflection probability
B) As classical electrons with random thermal motion
C) As separate Cooper pairs with independent tunnelling rates
D) In unison, as if a single particle filling the entire circuit
  • 28. What did superconductors used in Clarke, Martinis, and Devoret's experiment lack?
A) Energy gaps
B) Magnetic fields
C) Charged particles
D) Electrical resistance
  • 29. Who was aware of Mandelstam and Leontovich's findings while working on alpha decay?
A) Ronald Gurney
B) Lothar Nordheim
C) George Gamow
D) Edward Condon
  • 30. Whose derivation did Nordheim and Fowler simplify to find values for emitted currents and work functions that agreed with experiments?
A) Erwin Schrödinger
B) Walter Schottky
C) Friedrich Hund
D) J. Robert Oppenheimer
  • 31. Quantum tunnelling is a consequence of the wave nature of matter and what other factor?
A) Magnetic attraction
B) Quantum indeterminacy
C) Classical relativity
D) Thermal radiation
  • 32. Which equation describes the evolution of quantum wave functions?
A) Newton's second law
B) Schrödinger equation
C) Einstein's field equation
D) Maxwell's equations
  • 33. How does the probability of transmission of a wave packet through a barrier change as the barrier height increases?
A) It remains constant
B) It fluctuates randomly
C) It decreases exponentially
D) It increases linearly
  • 34. Tunnelling is seen most prominently in which type of particles?
A) High-density particles
B) Charged macroscopic objects
C) Neutral heavy elements
D) Low-mass particles
  • 35. Besides electrons and protons, tunnelling has been observed with what other entities?
A) Photons
B) Atoms
C) Neutron stars
D) Molecules of water
  • 36. What electronic application uses quantum tunnelling according to the text?
A) Vacuum tubes
B) Copper wiring
C) Resistors
D) Flash memory
  • 37. What microscope is mentioned as an application of tunnelling?
A) Scanning tunnelling microscope
B) Electron transmission microscope
C) Atomic force microscope
D) Light phase-contrast microscope
  • 38. What limits the minimum size of devices used in microelectronics?
A) Mechanical friction
B) Thermal expansion
C) Tunnelling
D) Optical diffraction
  • 39. At what approximate thickness do electrons tunnel readily through insulating layers and transistors?
A) Thinner than about 1 nm
B) Around 1 millimeter
C) Thicker than 10 nm
D) Exactly 5 micrometers
  • 40. When was the tunnelling effect predicted?
A) Late 19th century
B) Early 20th century
C) Early 21st century
D) Mid-19th century
  • 41. When did tunnelling achieve acceptance as a general physical phenomenon?
A) The 21st century
B) Mid-century
C) Early 20th century
D) Late 20th century
  • 42. Under which broader domain does quantum tunnelling fall?
A) Classical mechanics
B) Thermodynamics
C) Quantum mechanics
D) Acoustics
  • 43. In the conceptual comparison, particles attempting to travel across a potential barrier are compared to what?
A) A car driving through a tunnel
B) A wave crashing on a shore
C) A ball trying to roll over a hill
D) A pendulum swinging in a vacuum
  • 44. According to classical mechanics, what happens to a ball without sufficient energy to surmount a hill?
A) It tunnels through the hill
B) It stops and floats
C) It rolls back down
D) It teleports to the other side
  • 45. What describes the mere penetration of a wave function into a barrier without transmission on the other side?
A) Particle annihilation
B) Tunnelling effect
C) Wave collapse
D) Quantum entanglement
  • 46. What specifies everything that can be known about a physical system of particles?
A) The potential barrier
B) The Schrödinger equation
C) The WKB approximation
D) The wave function
  • 47. Which models of a tunnelling barrier can be analysed and solved algebraically?
A) Optical prisms
B) Rectangular barriers
C) Most complex problems
D) Semiclassical barriers
  • 48. What is used when most problems do not have an algebraic solution?
A) Visual animations
B) Critical angle calculations
C) Exact analytical formulas
D) Numerical solutions
  • 49. What offers approximate solutions that are easier to compute, such as the WKB approximation?
A) Algebraic formulations
B) Total internal reflection
C) Single photon counting
D) Semiclassical methods
  • 50. What physical phenomena does tunnelling help explain at a macroscopic level?
A) Macroscopic thermodynamic equilibrium
B) Only subatomic particle decay
C) Macroscopic gravitational waves
D) Important macroscopic physical phenomena
  • 51. What is tunnelling a source of in VLSI electronics?
A) Perfect electrical insulation
B) Increased signal speed
C) Current leakage
D) Enhanced magnetic shielding
  • 52. Tunnelling is considered the lower limit for what aspect of microelectronic devices?
A) How long their battery life lasts
B) How small they can be made
C) How fast their clock speed runs
D) How high their operating voltage can be
  • 53. What fundamental technique uses tunnelling to program flash memory?
A) Increasing depletion layer thickness
B) Programming floating gates
C) Cooling semiconductor junctions
D) Enhancing thermionic emission
  • 54. Cold emission materials are important for flash memory, vacuum tubes, and what other devices?
A) Incandescent light bulbs
B) Magnetic compasses
C) Standard alkaline batteries
D) Some electron microscopes
  • 55. Besides precision measurements, what other application uses Josephson junctions?
A) The standard relay switch
B) The multijunction solar cell
C) The incandescent light bulb
D) The cathode ray tube
  • 56. When can the depletion layer be thin enough for tunnelling in a diode?
A) When they are heavily doped
B) When they are cooled to absolute zero
C) When a magnetic field is applied
D) When the barrier thickness exceeds 3 nm
  • 57. When is the current due to tunnelling significant in a tunnel diode?
A) When the temperature is raised significantly
B) When a large reverse bias is applied
C) When a small forward bias is applied
D) When no voltage bias is present
  • 58. Where is the peculiar property of tunnel diodes (current decreasing as voltage increases) used?
A) High speed devices
B) Low frequency audio amplifiers
C) Long-range radio transmitters
D) High power heating elements
  • 59. What state is the resonant tunnelling diode in when no tunnelling occurs?
A) Open wire state
B) Superconducting state
C) Reverse bias
D) Cold emission state
  • 60. How do electrons flow once the two voltage energies align in a resonant tunnelling diode?
A) Like an exponential current leakage
B) Like an open wire
C) Like a thermionic emission
D) Like a blocked insulator
  • 61. What model of electrical conductivity does quantum tunnelling help further according to the text?
A) Drude-Lorentz model
B) Standard model
C) Drude-Binnig model
D) Bohr model
  • 62. The scanning tunnelling microscope operates by taking advantage of the relationship between quantum tunnelling and what variable?
A) Mass
B) Time
C) Temperature
D) Distance
  • 63. What components are used in an STM to adjust the height of the tip?
A) Piezoelectric rods
B) Thermal expansion wires
C) Hydraulic micro-pistons
D) Magnetic levitation springs
  • 64. What was the first application of quantum tunnelling?
A) Photosynthesis
B) Enzymatic catalysis
C) Proton decay
D) Radioactive decay
  • 65. Which hypothetical process might have quantum tunnelling as one of its mechanisms?
A) Nuclear fusion
B) Electron capture
C) Proton decay
D) Neutron scattering
  • 66. Which fundamental ion-molecule reaction in the interstellar medium involves hydrogen?
A) Formaldehyde with water ice
B) Oxygen ions with free electrons
C) Hydrogen ions with hydrogen molecules
D) Deuterium with helium nuclei
  • 67. What isotope was used alongside hydrogen in the ion trap experiment measuring tunnelling rates?
A) Tritium
B) Helium-3
C) Carbon-14
D) Deuterium
  • 68. What differences are generally attributed to the kinetic isotope effect when substituting isotopes?
A) Event horizon temperatures
B) Wave function amplitudes
C) Coulomb barrier heights
D) Zero-point vibrational energies
  • 69. Who developed a modified treatment of Arrhenius kinetics commonly used to model large isotopic effects requiring tunnelling?
A) Erwin Schrödinger
B) R. P. Bell
C) Albert Einstein
D) Per-Olov Lowdin
  • 70. Tunnelling of which molecule has been observed directly in the lab regarding interstellar clouds?
A) Water ice
B) Formaldehyde
C) Deuterium hydride
D) Molecular hydrogen
  • 71. In biology, electron tunnelling is a key factor in biochemical redox reactions and what other process?
A) Proton decay
B) Enzymatic catalysis
C) Cellular division
D) Spontaneous DNA mutation
  • 72. Proton tunnelling is a key factor in which biological phenomenon?
A) Enzymatic catalysis
B) Cellular respiration
C) Photosynthesis
D) Spontaneous DNA mutation
  • 73. What joins DNA base pairs together in a double helix?
A) A van der Waals interaction
B) A covalent peptide bond
C) An ionic salt bridge
D) A hydrogen bond
  • 74. What must a proton do for a spontaneous DNA mutation to occur?
A) Tunnel into the shallower well
B) Escape the DNA molecule completely
C) Absorb a photon from interstellar clouds
D) Tunnel into the deepest core of the nucleus
  • 75. What is the movement of a proton from its regular position in a DNA hydrogen bond called?
A) Evanescent coupling
B) Electron capture
C) A tautomeric transition
D) An isotopic substitution
  • 76. Who was the first to develop the theory of spontaneous mutation within the double helix involving proton tunnelling?
A) R. P. Bell
B) Erwin Schrödinger
C) Per-Olov Lowdin
D) Max Planck
  • 77. Where is quantum tunnelling expected to occur at the event horizon to produce Hawking radiation?
A) Black holes
B) Stellar cores
C) Interstellar clouds
D) Subsurface oceans
  • 78. What does quantum tunnelling give a small probability for emitting from a black hole?
A) Electrons for capture
B) Deuterium molecules
C) Heavy hydrogen ions
D) Radiation
  • 79. What does the symbol h-bar represent in the Schrödinger equation?
A) The potential energy
B) The reduced Planck constant
C) The Schrödinger wave function
D) The particle mass
  • 80. When M(x) is constant and negative, what do the solutions of the Schrödinger equation represent?
A) Stationary bound states
B) Rising and falling exponentials
C) Evanescent waves
D) Travelling waves
  • 81. In the analysis of M(x) signs, what does negative M(x) correspond to?
A) An event horizon
B) Medium B
C) Medium A
D) A potential barrier
  • 82. In the analysis of M(x) signs, what does positive M(x) correspond to?
A) Medium A
B) A travelling wave medium
C) Medium B
D) A circumstellar habitable zone
  • 83. What is noted about the ideas of Fröman and Fröman in relation to physics textbooks?
A) They were proven entirely mathematically false
B) Their ideas have not been incorporated into physics textbooks
C) They form the foundation of all modern quantum chemistry chapters
D) They completely replaced the Schrödinger equation
  • 84. What is denoted as A(x) and B(x) in the substitution step?
A) Complex-valued functions with zero real parts
B) Purely imaginary constants
C) Real-valued functions
D) Dimensionless scaling parameters
  • 85. To satisfy the real part of the equation, what is the minimum starting order of the power series in ħ?
A) ħ2
B) ħ-1
C) ħ1
D) ħ0
  • 86. Case 1 of the approximation corresponds to which physical phenomenon?
A) Infinite potential well confinement
B) Quantum tunnelling
C) Wave packet dispersion
D) Classical motion
  • 87. Where are both approximate solutions (Case 1 and Case 2) considered to be bad?
A) Far away from the potential hill
B) At the exact center of a rectangular barrier
C) Near the classical turning points
D) Where the particle energy is extremely high
  • 88. What is the definition of a classical turning point in terms of potential and energy?
A) E = V(x)
B) E > V(x)
C) E = 0
D) E < V(x)
  • 89. What kind of functions are used to solve the differential equation near a classical turning point?
A) Gaussian functions
B) Spherical harmonics
C) Airy functions
D) Legendre polynomials
  • 90. What represents the transmission coefficient for a particle tunnelling through a single potential barrier?
A) Φ(x)
B) R(E)
C) Ψ(x)
D) T(E)
  • 91. Whose experimental tunnelling time data of phonons, photons, and electrons was recently published?
A) Herbert Winful
B) Günter Nimtz
C) Francis E. Low
D) A. M. Steinberg
  • 92. Which physicist disputed the claims that particles could tunnel faster than light?
A) Francis E. Low
B) A. M. Steinberg
C) Günter Nimtz
D) Herbert Winful
  • 93. According to Herbert Winful, how does the wave packet of a tunnelling particle propagate?
A) Randomly
B) Non-locally
C) Instantly
D) Locally
  • 94. Can the group velocity be larger than the velocity of light during tunnelling?
A) Only in integrable systems
B) Yes
C) Only for photons
D) No
  • 95. What surrounds the two islands in the context of resonance-assisted tunnelling?
A) Linear magnetic fields
B) Nonlinear resonances
C) Electrostatic potential wells
D) Harmonic oscillators
  • 96. Evanescent wave coupling is an application of which equation to light?
A) The Schrödinger equation
B) Maxwell's wave-equation
C) The heat equation
D) The Navier-Stokes equation
  • 97. Acoustic waves on strings are related to quantum tunnelling through the application of what type of wave-equation?
A) Stochastic differential equation
B) Non-linear diffusion equation
C) Non-dispersive wave-equation
D) Dispersive quantum equation
  • 98. In the optical analogy of tunnelling, what material serves as medium A?
A) Water
B) Quartz
C) Vacuum
D) Glass
  • 99. In the optical analogy of tunnelling, what material serves as medium B (the barrier)?
A) Glass
B) Vacuum
C) Air
D) Free space
  • 100. In the acoustic analogy of tunnelling, what state of matter serves as medium B?
A) Liquid
B) Vacuum
C) Solid
D) Gas
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