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