PISA Type Test Items on Electron Wave Behavior
Exploring experimental evidence of electrons behaving as waves
Highlights
- Double-Slit Experiment: Reveals interference patterns that provide direct evidence of wave-like behavior in electrons.
- Electron Diffraction: Experiments such as the Davisson-Germer investigation confirm the predicted wavelength of electrons.
- Wave-Particle Duality: Both experimental observations and theoretical constructs (like de Broglie's hypothesis) illustrate that electrons exhibit dual properties.
Test Item Overview
The following 10 PISA-type multiple-choice test items are designed to assess students' understanding of experimental evidence supporting the wave-like behavior of electrons. Each item includes a clear stem, answer options, and where applicable, an illustration prompt to enhance conceptual understanding.
Test Items
Item 1: The Davisson-Germer Experiment
Stem
The Davisson-Germer experiment provided pioneering evidence for electron wave behavior by measuring electron diffraction off a crystalline nickel target. Which observation in this experiment confirms the wave-like nature of electrons?
Options
- A) Electrons were deflected by electric fields only.
- B) Electrons produced a diffraction pattern when scattered by a nickel crystal.
- C) Electrons increased in speed when exposed to high voltage.
- D) Electrons generated magnetic fields around the target.
Correct Answer
B) Electrons produced a diffraction pattern when scattered by a nickel crystal.
Illustration: Diagram showing electrons striking a nickel crystal and forming a series of diffraction spots on a detector screen.
Item 2: Double-Slit Experiment
Stem
In the double-slit experiment, electrons demonstrate wave-particle duality. What pattern is typically observed on the detection screen when a large number of electrons are allowed to pass through two slits without being individually observed?
Options
- A) Two distinct impact spots corresponding to each slit.
- B) A uniform scattered pattern.
- C) An interference pattern of alternating bright and dark bands.
- D) A completely random impact distribution.
Correct Answer
C) An interference pattern of alternating bright and dark bands.
Illustration: A schematic of the double-slit setup showing electrons emerging through two slits and interfering constructively and destructively to form a fringe pattern.
Item 3: De Broglie Hypothesis
Stem
Louis de Broglie proposed that all matter has an intrinsic wavelength. What experimental observation best supports de Broglie’s hypothesis regarding electrons?
Options
- A) Electrons generate thermal energy in conductors.
- B) Electron beams form diffraction patterns when passed through a crystal lattice.
- C) Electrons accelerate in a vacuum tube.
- D) Electrons create a magnetic field when in motion.
Correct Answer
B) Electron beams form diffraction patterns when passed through a crystal lattice.
Illustration: A visual representation of electron beams interacting with a crystal, resulting in a diffraction pattern that maps de Broglie wavelengths to momentum.
Item 4: Electron Diffraction Patterns
Stem
In electron diffraction experiments, electrons are shown to bend around obstacles similarly to waves. What does the appearance of distinct fringes in these experiments indicate?
Options
- A) Electrons always behave as particles.
- B) Electrons lose energy when colliding with atoms.
- C) Electrons have a dual nature, exhibiting wave-like properties.
- D) Electrons cannot interact with crystal structures.
Correct Answer
C) Electrons have a dual nature, exhibiting wave-like properties.
Illustration: An image depicting an electron beam passing through a thin crystalline film producing a set of diffraction rings or fringes on a detection screen.
Item 5: Interference vs. Observation
Stem
During the double-slit experiment, what effect does placing detectors at the slits (to determine which path an electron takes) have on the resulting pattern?
Options
- A) It enhances the contrast in the interference pattern.
- B) It causes the interference pattern to disappear, revealing particle-like impacts.
- C) It doubles the number of fringes.
- D) It has no observable effect on the pattern.
Correct Answer
B) It causes the interference pattern to disappear, revealing particle-like impacts.
Illustration: Diagram comparing the electron impact distribution on a screen with and without detectors at the slits.
Item 6: Quantum Mechanics and Probability
Stem
Quantum mechanics introduces the concept of probability wave functions. When squared, these wave functions represent the probability density of finding an electron. Which experimental setup primarily demonstrates this probabilistic behavior?
Options
- A) The use of electron microscopes for imaging.
- B) The single-slit diffraction experiment.
- C) Observations in the double-slit experiment without path detection.
- D) Rutherford's gold foil experiment.
Correct Answer
C) Observations in the double-slit experiment without path detection.
Illustration: A graph or diagram showing a probability density distribution derived from the squared wave function in a double-slit setup.
Item 7: Role of Momentum
Stem
According to de Broglie, the wavelength (\( \lambda \)) associated with an electron is given by \( \lambda = \frac{h}{p} \), where \( h \) is Planck’s constant and \( p \) is momentum. Which experimental observation reflects the validity of this relationship?
Options
- A) Changes in interference fringe spacing when electron velocity is varied.
- B) A constant fringe spacing regardless of electron speed.
- C) A proportional increase in electron speed with current.
- D) The generation of secondary electrons upon collision.
Correct Answer
A) Changes in interference fringe spacing when electron velocity is varied.
Illustration: A schematic showing how varying electron momentum alters the diffraction fringe spacing in an interference pattern, in accordance with the equation \( \lambda = \frac{h}{p} \).
Item 8: Electron Microscopy Evidence
Stem
Electron microscopes rely on the wave-like behavior of electrons to achieve high resolution. What property of electrons is primarily responsible for this capability?
Options
- A) Their large mass compared to photons.
- B) Their ability to be focused using magnetic lenses.
- C) Their associated wavelength which can be much shorter than visible light.
- D) Their charge which interacts with the specimen.
Correct Answer
C) Their associated wavelength which can be much shorter than visible light.
Illustration: Diagram of an electron microscope showing a beam of electrons and highlighting the short de Broglie wavelength exploited to resolve small details.
Item 9: Observing Wave-Particle Duality
Stem
The concept of wave-particle duality is fundamental in quantum mechanics. Which experiment best exemplifies the simultaneous demonstration of electron wave-like behavior and particle-like impacts?
Options
- A) The photoelectric effect experiment.
- B) Rutherford's scattering experiment.
- C) The double-slit experiment without path detection.
- D) Compton scattering.
Correct Answer
C) The double-slit experiment without path detection.
Illustration: Side-by-side images showing a clear interference pattern contrasted with the distribution of individual electron impacts when path detection is applied.
Item 10: Comprehensive Evidence in Quantum Experiments
Stem
Several experiments have contributed to our understanding of the wave-like properties of electrons. Which combination of experiments best encapsulates the experimental evidence for electron wave behavior?
Options
- A) Davisson-Germer experiment and the Compton scattering experiment.
- B) Double-slit experiment and electron diffraction experiments.
- C) Photoelectric effect experiment and Rutherford's gold foil experiment.
- D) Rutherford scattering experiment and electron microscopy.
Correct Answer
B) Double-slit experiment and electron diffraction experiments.
Illustration: A combined diagram that merges elements of the double-slit interference and electron diffraction scenarios, effectively showing both experimental frameworks that support wave-particle duality.
Table: Overview of Key Experiments Demonstrating Wave Behavior
| Experiment | Key Observation | Concept Demonstrated |
|---|---|---|
| Davisson-Germer Experiment | Diffraction pattern from a crystal | Electron wave nature |
| Double-Slit Experiment | Interference fringes when electrons pass through slits | Wave-particle duality |
| Electron Diffraction | Diffraction rings or fringes formed by electrons | De Broglie wavelength |
| Electron Microscopy | High resolution from short electron wavelengths | Application of wave behavior |
References
- Davisson–Germer Experiment - Wikipedia
- Wave–Particle Duality - Wikipedia
- de Broglie Waves - LibreTexts
- Experimental Evidence - SlideShare
- Electron Diffraction - APS Physics
Recommended Searches
- Explore detailed analyses of the double-slit experiment with electrons
- Learn more about the Davisson-Germer experiment and its implications
- Understand de Broglie's hypothesis and experimental confirmations
- Investigate how electron wave properties enhance microscopy resolution
- Delve into the concept of wave-particle duality in quantum mechanics
Last updated March 18, 2025