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