Quantum tunnelling - Quiz
  • 1. In what year was the Schrödinger equation published?
A) 1925
B) 1928
C) 1926
D) 1927
  • 2. Who was the first person to apply the Schrödinger equation to a problem involving tunnelling?
A) Leonid Mandelstam
B) Erwin Schrödinger
C) George Gamow
D) Friedrich Hund
  • 3. What physical system did Friedrich Hund study while investigating tunnelling in 1927?
A) An infinite potential well
B) A single-well potential
C) A double-well potential
D) A semiconductor diode
  • 4. Who discovered tunnelling independently alongside Mikhail Leontovich and published their results in 1928?
A) Ralph Fowler
B) Yakov Frenkel
C) Lothar Nordheim
D) Leonid Mandelstam
  • 5. Who assisted Lothar Nordheim in publishing a paper discussing thermionic emission in 1927?
A) Walter Schottky
B) Brian Josephson
C) J. Robert Oppenheimer
D) Ralph Fowler
  • 6. What did Lothar Nordheim's 1927 paper discuss?
A) Alpha decay half-lives
B) Scanning tunnelling microscopy
C) Thermionic emission and reflection of electrons from metals
D) Superconducting energy gaps
  • 7. According to classical physics, what is the probability that an electron transmits or reflects at a surface barrier?
A) 50%
B) 0%
C) 100%
D) Variable
  • 8. In what year did J. Robert Oppenheimer publish two papers on field emission?
A) 1931
B) 1927
C) 1926
D) 1928
  • 9. What phenomenon did J. Robert Oppenheimer study in his 1928 papers?
A) Superconductivity
B) Field emission
C) Alpha decay
D) Thermionic emission
  • 10. Who provided a mathematical explanation for alpha decay in 1928?
A) Friedrich Hund and Leonid Mandelstam
B) George Gamow, Ronald Gurney, and Edward Condon
C) Leo Esaki and Ivar Giaever
D) Lothar Nordheim and Ralph Fowler
  • 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 temperature and electrical resistance
D) Between the half-life of the particle and the energy of emission
  • 12. What German term for the tunnel effect was used by Walter Schottky in 1931?
A) Wellenmechanischer Tunneleffekt
B) Tunneleffekt
C) Quantenbarriere
D) Tunnelierung
  • 13. Who introduced the English term 'tunnel effect' in a textbook in 1932?
A) Yakov Frenkel
B) Lothar Nordheim
C) George Gamow
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) Leo Esaki
B) Brian Josephson
C) Gerd Binnig
D) Ivar Giaever
  • 16. What type of device did Leo Esaki develop based on the tunnel effect?
A) A scanning tunnelling microscope
B) A thermionic emitter
C) A superconductor circuit
D) A diode
  • 17. Who showed experimentally that tunnelling also took place in superconductors in 1960?
A) Heinrich Rohrer
B) Brian Josephson
C) Leo Esaki
D) Ivar Giaever
  • 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) Brian Josephson
B) John Clarke
C) Leo Esaki
D) Ivar Giaever
  • 20. Which scientists shared the 1973 Nobel Prize in Physics for their works on quantum tunnelling in solids?
A) Gamow, Gurney, and Condon
B) Clarke, Martinis, and Devoret
C) Esaki, Giaever, and Josephson
D) Binnig, Rohrer, and Esaki
  • 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) Detecting alpha decay half-lives
B) Imaging surfaces at the atomic level
C) Observing macroscopic quantum circuits
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) 2025
C) 1986
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) John Clarke, John M. Martinis, and Michel H. Devoret
D) George Gamow, Ronald Gurney, and Edward Condon
  • 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 scanning tip and an atomic surface
C) A double-well potential and an electron emitter
D) Two semiconductor diodes separated by a nanometre barrier
  • 27. In the macroscopic tunnelling experiments, how did the charged particles in the superconductor behave?
A) Individually with a 100% reflection probability
B) In unison, as if a single particle filling the entire circuit
C) As separate Cooper pairs with independent tunnelling rates
D) As classical electrons with random thermal motion
  • 28. What did superconductors used in Clarke, Martinis, and Devoret's experiment lack?
A) Charged particles
B) Energy gaps
C) Magnetic fields
D) Electrical resistance
  • 29. Who was aware of Mandelstam and Leontovich's findings while working on alpha decay?
A) Edward Condon
B) Ronald Gurney
C) George Gamow
D) Lothar Nordheim
  • 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) Magnetic attraction
B) Classical relativity
C) Quantum indeterminacy
D) Thermal radiation
  • 32. Which equation describes the evolution of quantum wave functions?
A) Einstein's field equation
B) Newton's second law
C) Maxwell's equations
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 decreases exponentially
B) It increases linearly
C) It fluctuates randomly
D) It remains constant
  • 34. Tunnelling is seen most prominently in which type of particles?
A) Charged macroscopic objects
B) High-density particles
C) Neutral heavy elements
D) Low-mass particles
  • 35. Besides electrons and protons, tunnelling has been observed with what other entities?
A) Atoms
B) Molecules of water
C) Neutron stars
D) Photons
  • 36. What electronic application uses quantum tunnelling according to the text?
A) Copper wiring
B) Vacuum tubes
C) Resistors
D) Flash memory
  • 37. What microscope is mentioned as an application of tunnelling?
A) Light phase-contrast microscope
B) Scanning tunnelling microscope
C) Electron transmission microscope
D) Atomic force microscope
  • 38. What limits the minimum size of devices used in microelectronics?
A) Tunnelling
B) Thermal expansion
C) Mechanical friction
D) Optical diffraction
  • 39. At what approximate thickness do electrons tunnel readily through insulating layers and transistors?
A) Exactly 5 micrometers
B) Thinner than about 1 nm
C) Thicker than 10 nm
D) Around 1 millimeter
  • 40. When was the tunnelling effect predicted?
A) Early 21st century
B) Early 20th century
C) Late 19th century
D) Mid-19th century
  • 41. When did tunnelling achieve acceptance as a general physical phenomenon?
A) Late 20th century
B) The 21st century
C) Mid-century
D) Early 20th century
  • 42. Under which broader domain does quantum tunnelling fall?
A) Quantum mechanics
B) Thermodynamics
C) Classical 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 ball trying to roll over a hill
C) A pendulum swinging in a vacuum
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 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) Tunnelling effect
B) Particle annihilation
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 wave function
D) The WKB approximation
  • 47. Which models of a tunnelling barrier can be analysed and solved algebraically?
A) Rectangular barriers
B) Optical prisms
C) Semiclassical barriers
D) Most complex problems
  • 48. What is used when most problems do not have an algebraic solution?
A) Visual animations
B) Critical angle calculations
C) Numerical solutions
D) Exact analytical formulas
  • 49. What offers approximate solutions that are easier to compute, such as the WKB approximation?
A) Algebraic formulations
B) Single photon counting
C) Total internal reflection
D) Semiclassical methods
  • 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) Current leakage
C) Enhanced magnetic shielding
D) Perfect electrical insulation
  • 52. Tunnelling is considered the lower limit for what aspect of microelectronic devices?
A) How high their operating voltage can be
B) How small they can be made
C) How long their battery life lasts
D) How fast their clock speed runs
  • 53. What fundamental technique uses tunnelling to program flash memory?
A) Programming floating gates
B) Increasing depletion layer thickness
C) Enhancing thermionic emission
D) Cooling semiconductor junctions
  • 54. Cold emission materials are important for flash memory, vacuum tubes, and what other devices?
A) Standard alkaline batteries
B) Magnetic compasses
C) Some electron microscopes
D) Incandescent light bulbs
  • 55. Besides precision measurements, what other application uses Josephson junctions?
A) The multijunction solar cell
B) The standard relay switch
C) The cathode ray tube
D) The incandescent light bulb
  • 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 the barrier thickness exceeds 3 nm
D) When they are heavily doped
  • 57. When is the current due to tunnelling significant in a tunnel diode?
A) When a large reverse bias is applied
B) When a small forward bias is applied
C) When the temperature is raised significantly
D) When no voltage bias is present
  • 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 speed devices
D) High power heating elements
  • 59. What state is the resonant tunnelling diode in when no tunnelling occurs?
A) Cold emission state
B) Superconducting state
C) Reverse bias
D) Open wire state
  • 60. How do electrons flow once the two voltage energies align in a resonant tunnelling diode?
A) Like a blocked insulator
B) Like an exponential current leakage
C) Like a thermionic emission
D) Like an open wire
  • 61. What model of electrical conductivity does quantum tunnelling help further according to the text?
A) Drude-Binnig model
B) Drude-Lorentz model
C) Standard model
D) Bohr model
  • 62. The scanning tunnelling microscope operates by taking advantage of the relationship between quantum tunnelling and what variable?
A) Distance
B) Time
C) Mass
D) Temperature
  • 63. What components are used in an STM to adjust the height of the tip?
A) Thermal expansion wires
B) Hydraulic micro-pistons
C) Magnetic levitation springs
D) Piezoelectric rods
  • 64. What was the first application of quantum tunnelling?
A) Enzymatic catalysis
B) Photosynthesis
C) Radioactive decay
D) Proton decay
  • 65. Which hypothetical process might have quantum tunnelling as one of its mechanisms?
A) Electron capture
B) Proton decay
C) Neutron scattering
D) Nuclear fusion
  • 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) Carbon-14
B) Deuterium
C) Helium-3
D) Tritium
  • 68. What differences are generally attributed to the kinetic isotope effect when substituting isotopes?
A) Wave function amplitudes
B) Zero-point vibrational energies
C) Event horizon temperatures
D) Coulomb barrier heights
  • 69. Who developed a modified treatment of Arrhenius kinetics commonly used to model large isotopic effects requiring tunnelling?
A) Erwin Schrödinger
B) Per-Olov Lowdin
C) R. P. Bell
D) Albert Einstein
  • 70. Tunnelling of which molecule has been observed directly in the lab regarding interstellar clouds?
A) Deuterium hydride
B) Molecular hydrogen
C) Formaldehyde
D) Water ice
  • 71. In biology, electron tunnelling is a key factor in biochemical redox reactions and what other process?
A) Enzymatic catalysis
B) Spontaneous DNA mutation
C) Cellular division
D) Proton decay
  • 72. Proton tunnelling is a key factor in which biological phenomenon?
A) Cellular respiration
B) Enzymatic catalysis
C) Spontaneous DNA mutation
D) Photosynthesis
  • 73. What joins DNA base pairs together in a double helix?
A) An ionic salt bridge
B) A hydrogen bond
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) Escape the DNA molecule completely
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) Per-Olov Lowdin
B) R. P. Bell
C) Erwin Schrödinger
D) Max Planck
  • 77. Where is quantum tunnelling expected to occur at the event horizon to produce Hawking radiation?
A) Black holes
B) Interstellar clouds
C) Stellar cores
D) Subsurface oceans
  • 78. What does quantum tunnelling give a small probability for emitting from a black hole?
A) Heavy hydrogen ions
B) Deuterium molecules
C) Electrons for capture
D) Radiation
  • 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) Rising and falling exponentials
B) Evanescent waves
C) Stationary bound states
D) Travelling waves
  • 81. In the analysis of M(x) signs, what does negative M(x) correspond to?
A) Medium B
B) An event horizon
C) A potential barrier
D) Medium A
  • 82. In the analysis of M(x) signs, what does positive M(x) correspond to?
A) Medium B
B) Medium A
C) A travelling wave medium
D) A circumstellar habitable zone
  • 83. What is noted about the ideas of Fröman and Fröman in relation to physics textbooks?
A) They form the foundation of all modern quantum chemistry chapters
B) They were proven entirely mathematically false
C) They completely replaced the Schrödinger equation
D) Their ideas have not been incorporated into physics textbooks
  • 84. What is denoted as A(x) and B(x) in the substitution step?
A) Purely imaginary constants
B) Dimensionless scaling parameters
C) Real-valued functions
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) ħ-1
C) ħ1
D) ħ0
  • 86. Case 1 of the approximation corresponds to which physical phenomenon?
A) Classical motion
B) Wave packet dispersion
C) Quantum tunnelling
D) Infinite potential well confinement
  • 87. Where are both approximate solutions (Case 1 and Case 2) considered to be bad?
A) Near the classical turning points
B) Where the particle energy is extremely high
C) At the exact center of a rectangular barrier
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) Airy functions
C) Gaussian functions
D) Legendre polynomials
  • 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) A. M. Steinberg
B) Günter Nimtz
C) Francis E. Low
D) Herbert Winful
  • 92. Which physicist disputed the claims that particles could tunnel faster than light?
A) Herbert Winful
B) A. M. Steinberg
C) Günter Nimtz
D) Francis E. Low
  • 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) Yes
B) Only in integrable systems
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) Harmonic oscillators
D) Electrostatic potential wells
  • 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) Dispersive quantum equation
B) Non-dispersive wave-equation
C) Non-linear diffusion equation
D) Stochastic differential equation
  • 98. In the optical analogy of tunnelling, what material serves as medium A?
A) Vacuum
B) Water
C) Quartz
D) Glass
  • 99. In the optical analogy of tunnelling, what material serves as medium B (the barrier)?
A) Glass
B) Vacuum
C) Free space
D) Air
  • 100. In the acoustic analogy of tunnelling, what state of matter serves as medium B?
A) Gas
B) Solid
C) Vacuum
D) Liquid
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