AP Physics Questions on Wave-Particle Duality

📚 Quick Study Guide

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• Wave-Particle Duality: The concept that every elementary particle or quantum entity exhibits the properties of both particles and waves.
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• Wave Nature: Demonstrated by phenomena like diffraction and interference.
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• Particle Nature: Exhibited through discrete interactions, such as in the photoelectric effect and Compton scattering.
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• de Broglie Wavelength: The wavelength associated with a particle of momentum $p$ is given by $\lambda = \frac{h}{p}$, where $h$ is Planck's constant ($6.626 \times 10^{-34} \text{ J s}$).
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• Photoelectric Effect: Emission of electrons when electromagnetic radiation hits a material. The energy of the photon must exceed the work function ($\phi$) of the material: $E = hf = \phi + KE_{\text{max}}$.
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• Heisenberg Uncertainty Principle: States that certain pairs of physical properties, like position and momentum, cannot be simultaneously known to arbitrarily high precision: $\Delta x \Delta p \geq \frac{h}{4\pi}$.

🧪 Practice Quiz

1. Which of the following phenomena best demonstrates the wave nature of electrons?
   1. A) Photoelectric effect
   2. B) Compton scattering
   3. C) Electron diffraction
   4. D) Blackbody radiation
2. What is the de Broglie wavelength of an electron with a momentum of $3.313 \times 10^{-24} \text{ kg m/s}$?
   1. A) $0.5 \times 10^{-10} \text{ m}$
   2. B) $1.0 \times 10^{-10} \text{ m}$
   3. C) $2.0 \times 10^{-10} \text{ m}$
   4. D) $4.0 \times 10^{-10} \text{ m}$
3. In the photoelectric effect, increasing the intensity of the incident light will:
   1. A) Increase the kinetic energy of the emitted electrons
   2. B) Decrease the kinetic energy of the emitted electrons
   3. C) Increase the number of emitted electrons
   4. D) Decrease the number of emitted electrons
4. Which of the following statements is most accurate regarding wave-particle duality?
   1. A) Particles always behave as particles, and waves always behave as waves.
   2. B) Particles sometimes behave as waves, and waves sometimes behave as particles.
   3. C) Particles only behave as waves when observed.
   4. D) Waves only behave as particles when observed.
5. According to the Heisenberg Uncertainty Principle, if the uncertainty in the position of a particle decreases, the uncertainty in its momentum:
   1. A) Increases
   2. B) Decreases
   3. C) Remains the same
   4. D) Becomes zero
6. What is the energy of a photon with a wavelength of $500 \text{ nm}$? (Planck's constant $h = 6.626 \times 10^{-34} \text{ J s}$, speed of light $c = 3 \times 10^8 \text{ m/s}$)
   1. A) $1.99 \times 10^{-19} \text{ J}$
   2. B) $3.98 \times 10^{-19} \text{ J}$
   3. C) $5.97 \times 10^{-19} \text{ J}$
   4. D) $7.96 \times 10^{-19} \text{ J}$
7. The Compton effect demonstrates which property of light?
   1. A) Wave nature
   2. B) Particle nature
   3. C) Interference
   4. D) Diffraction