12.2.1 Understanding wave-particle duality

• Particles have a wavelength associated with them.

  False
• The de Broglie hypothesis relates a particle's wavelength to its momentum
• Match the wave-particle duality property with its description:

  Wave ↔️ Continuous oscillation

  Particle ↔️ Discrete entity

  Electron ↔️ Exhibits both properties
• The photoelectric effect demonstrates the particle nature of light.

  True
• Match the light theory with its key property:

  Wave theory ↔️ Energy is proportional to amplitude squared

  Particle theory ↔️ Energy is proportional to frequency
• The photoelectric effect demonstrates that light interacts with matter as a stream of particles.


  True
• The wave theory of light can fully explain all observations related to light's interaction with matter.

  False
• Order the key observations from the photoelectric effect.

  1️⃣ Electron energy depends on light frequency

  2️⃣ Electrons are emitted instantaneously

  3️⃣ A minimum frequency is required
• The wave-particle duality of light is a fundamental concept in quantum mechanics.


  True
• Match the wave or particle property with its characteristic.

  Wavelength (λ) ↔️ Distance between peaks

  Momentum (p) of a particle ↔️ p = mv

  Momentum (p) of a wave ↔️ p = h/λ
• What is the energy formula for particles according to wave-particle duality?

  $E =$$mc^{2}$
• In the double-slit experiment with electrons, an interference pattern is observed.
• The double-slit experiment with electrons demonstrates their wave-like
• Which experiment demonstrates the particle nature of light?

  Photoelectric effect
• The minimum frequency required to eject electrons is called the threshold frequency.
• Light behaves as a continuous wave in the photoelectric effect.

  False
• Waves are discrete entities, while particles are continuous oscillations.

  False
• The Davisson-Germer experiment showed that the measured wavelength matched De Broglie's prediction.


  True
• Wave-particle duality challenges classical intuitions about matter and energy.


  True
• The wave nature of quantum objects is characterized by continuous oscillation
• Match the examples with their associated wave-particle duality property:

  Light ↔️ Waves

  Electrons ↔️ Particles
• The de Broglie wavelength is inversely proportional to momentum.

  True
• Which experiment confirms the wave-like behavior of electrons?

  Double-slit experiment
• In the photoelectric effect, light is treated as a stream of discrete particles called photons
• In the formula $E =$$hf$, *h* is known as Planck's constant
• The particle theory of light explains the photoelectric effect by requiring a minimum frequency
• What is the key experiment that demonstrates the particle nature of light?

  Photoelectric effect
• What are the discrete packets of energy that make up light in the particle theory called?

  Photons
• De Broglie's hypothesis supports the wave-particle duality of quantum objects.


  True
• The nature of waves is described as a continuous oscillation.
• What experimental evidence supports the wave properties of electrons?

  Double-slit experiment
• What is the key equation in De Broglie's hypothesis relating wavelength and momentum?

  $\lambda =$$\frac{h}{p}$
• The wavelength of a wave is the distance between its peaks
• What is the key observation regarding electron emission time in the photoelectric effect?

  Instantaneous emission
• Match the property with its correct theory:

  Energy in wave theory ↔️ E ∝ A²

  Energy in particle theory ↔️ E = hf

  Interaction in wave theory ↔️ Gradual absorption

  Interaction in particle theory ↔️ Instantaneous emission
• De Broglie's hypothesis supports the idea that quantum objects exhibit wave-particle duality
• In the Davisson-Germer experiment, electrons were fired at a nickel crystal
• In quantum mechanics, the position and momentum of a quantum object cannot both be precisely determined, according to the principle of uncertainty
• What does wave-particle duality refer to?

  Wave and particle properties
• What is the energy formula for waves in wave-particle duality?

  $E =$$hf$