Questions About the de Broglie Wave Equation

Questions About the de Broglie Wave Equation

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Multiple-Choice Questions

1. What does the de Broglie wavelength equation relate?
   A) Energy and mass
   B) Force and acceleration
   C) Mass and charge
   D) Wavelength and momentum
   E) Speed and energy

2. Which of the following is the correct de Broglie wave equation?
   A) $\lambda = \frac{E}{mc^2}$
   B) $\lambda = \frac{mc}{h}$
   C) $\lambda = \frac{h}{p}$
   D) $\lambda = \frac{p}{h}$
   E) $\lambda = \frac{h}{mv^2}$

3. What does $h$ represent in the de Broglie equation?
   A) Planck's time constant
   B) Gravitational constant
   C) Boltzmann constant
   D) Planck's constant
   E) Avogadro’s number

4. What are the units of de Broglie wavelength?
   A) Seconds
   B) Meters
   C) Kilograms
   D) Joules
   E) Meters/second

5. Which physical property of a particle determines its de Broglie wavelength?
   A) Charge
   B) Mass
   C) Momentum
   D) Temperature
   E) Volume

6. According to de Broglie, which of the following can exhibit wave-like behavior?
   A) Only photons
   B) Only electrons
   C) Only atoms
   D) Only charged particles
   E) All matter

7. As the momentum of a particle increases, what happens to its de Broglie wavelength?
   A) Increases
   B) Decreases
   C) Remains constant
   D) Becomes zero
   E) Becomes infinite

8. Which experiment confirmed the wave-like behavior of electrons?
   A) Millikan oil drop experiment
   B) Rutherford gold foil experiment
   C) Davisson-Germer experiment
   D) Stern-Gerlach experiment
   E) Photoelectric effect

9. The de Broglie wavelength of a particle is inversely proportional to:
   A) Frequency
   B) Energy
   C) Velocity
   D) Momentum
   E) Wavelength

10. Which condition must be met for de Broglie waves to be observable?
    A) The particle must be stationary
    B) The particle must be electrically neutral
    C) The particle must be moving at the speed of light
    D) The particle must have very low mass and high speed
    E) The particle must be in a vacuum

11. The de Broglie wavelength of an electron is shorter than that of a proton when:
    A) Both are at rest
    B) Both have the same momentum
    C) Both have the same energy
    D) The electron has less speed
    E) The electron has more mass

12. If a particle has zero momentum, what is its de Broglie wavelength?
    A) Zero
    B) Infinite
    C) Equal to Planck’s constant
    D) Cannot be determined
    E) Equal to the speed of light

13. What is the momentum of a particle with a de Broglie wavelength of $1 \times 10^{-10}$ m? (Take $h = 6.626 \times 10^{-34}$ Js)
    A) $6.626 \times 10^{-44}$ kg·m/s
    B) $6.626 \times 10^{-24}$ kg·m/s
    C) $6.626 \times 10^{-10}$ kg·m/s
    D) $6.626 \times 10^{10}$ kg·m/s
    E) $6.626 \times 10^{-34}$ kg·m/s

14. Which of the following is NOT a consequence of de Broglie’s hypothesis?
    A) Electron diffraction
    B) Quantum tunneling
    C) Atomic spectra
    D) Photoelectric effect
    E) Electron interference

15. Which value of de Broglie wavelength corresponds to higher energy?
    A) 100 m
    B) 1 m
    C) 0.1 m
    D) 1 nm
    E) 1 km

16. De Broglie hypothesis bridges which two areas of physics?
    A) Classical mechanics and thermodynamics
    B) Quantum mechanics and general relativity
    C) Classical mechanics and quantum mechanics
    D) Thermodynamics and optics
    E) Electrodynamics and mechanics

17. What kind of waves are associated with particles in de Broglie’s theory?
    A) Electromagnetic waves
    B) Longitudinal mechanical waves
    C) Standing waves
    D) Matter waves
    E) Gravitational waves

18. What determines the observability of de Broglie waves in an experiment?
    A) Temperature of the system
    B) Speed of light
    C) Wavelength relative to object size
    D) Volume of the container
    E) Number of particles

19. In what kind of system is de Broglie wavelength most significant?
    A) Large macroscopic objects
    B) Low-energy systems
    C) High-momentum systems
    D) Microscopic particles like electrons
    E) Objects at rest

20. The de Broglie wavelength of a neutron (mass $m$) traveling at speed $v$ is:
    A) $\lambda = h \cdot m \cdot v$
    B) $\lambda = \frac{mv}{h}$
    C) $\lambda = \frac{h}{mv}$
    D) $\lambda = \frac{h}{m + v}$
    E) $\lambda = \frac{m}{hv}$

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Answers and Explanations

1. D – It relates wavelength and momentum.

2. C – $\lambda = \frac{h}{p}$ is the de Broglie equation.

3. D – $h$ is Planck’s constant (~$6.626 \times 10^{-34}$ Js).

4. B – Wavelength is measured in meters.

5. C – Wavelength depends on momentum $p = mv$.

6. E – All matter has wave-like behavior according to de Broglie.

7. B – As momentum increases, wavelength decreases.

8. C – Davisson and Germer demonstrated electron diffraction.

9. D – Wavelength is inversely proportional to momentum.

10. D – Low mass and high speed make wave effects detectable.

11. C – For equal energy, electron’s lower mass gives longer wavelength.

12. B – If momentum is zero, wavelength is infinite.

13. B – $p = \frac{h}{\lambda} = \frac{6.626 \times 10^{-34}}{1 \times 10^{-10}} = 6.626 \times 10^{-24}$ kg·m/s.

14. D – The photoelectric effect is not a direct consequence of de Broglie hypothesis.

15. D – Shorter wavelength (1 nm) indicates higher momentum/energy.

16. C – It connects classical and quantum mechanics.

17. D – De Broglie introduced matter waves.

18. C – The wavelength must be comparable to object size for effects to be visible.

19. D – Wave behavior is significant for small, fast particles like electrons.

20. C – By de Broglie: $\lambda = \frac{h}{mv}$.

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Ronaldo Silva: Professor and Specialist in Science Teaching, from UFF/RJ, with more than 25 years of experience in teaching.