Quantum Theory and Wave–Particle Duality - AP Physics 2

1. Which experiment demonstrated the wave nature of electrons?

   Davisson-Germer experiment. Electron diffraction confirmed de Broglie's matter wave hypothesis.

2. Which constant appears in both $E = hf$ and $\lambda = \frac{h}{p}$?

   Planck's constant, $h$. Universal quantum constant in energy and wave relations.

3. What phenomenon does the photoelectric effect explain?

   Ejection of electrons by light. Light removes electrons from material surfaces.

4. What does the Heisenberg uncertainty principle state?

   $\Delta x \Delta p \geq \frac{\hbar}{2}$. Position and momentum cannot both be precisely known simultaneously.

5. Find the energy of a photon with wavelength $\lambda = 500 \text{ nm}$.

   Use $E = \frac{hc}{\lambda}$. Substitute wavelength into energy-wavelength relationship.

6. What is the relationship between wavelength and frequency?

   Inversely proportional, $c = f\lambda$. Higher frequency means shorter wavelength for constant speed.

7. What is the photoelectric effect?

   Emission of electrons when light hits a material. Light-induced electron emission from metal surfaces.

8. State Planck's constant value.

   6.62607015 × $10^{-34}$ Js. Fundamental constant relating energy to frequency in quantum mechanics.

9. Determine the frequency of a photon with energy $E$.

   $f = \frac{E}{h}$. Rearranged form of $E = hf$ to solve for frequency.

10. Convert $\lambda = 450 \text{ nm}$ to energy of a photon.

    $E = \frac{hc}{\lambda}$. Apply energy-wavelength formula with given wavelength value.

11. What does $\lambda$ represent in de Broglie wavelength?

    Wavelength of a particle. Matter wavelength in de Broglie's wave hypothesis.

12. What is the work function $\phi$?

    Minimum energy needed to remove an electron from a material. Energy threshold for electron emission from surface.

13. What is the wave-particle duality concept?

    Particles exhibit both wave-like and particle-like properties. Fundamental quantum principle describing matter and energy behavior.

14. How are wavelength and momentum related in de Broglie's hypothesis?

    Inversely proportional, $\lambda = \frac{h}{p}$. Higher momentum gives shorter wavelength.

15. Identify the relationship for kinetic energy of ejected electrons.

    $KE = hf - \phi$. Einstein's photoelectric equation for electron kinetic energy.

16. State the formula for calculating momentum $p$ of a photon.

    $p = \frac{h}{\lambda}$. Photon momentum derived from de Broglie wavelength relation.

17. What is the relationship between energy and frequency of a photon?

    $E = hf$. Planck's quantum energy formula for photons.

18. What effect does increasing photon frequency have on its wavelength?

    Wavelength decreases. Inverse relationship from $c = f\lambda$ at constant speed.

19. What is the de Broglie wavelength formula?

    $\lambda = \frac{h}{p}$. Relates particle wavelength to momentum through Planck's constant.

20. What does a higher frequency imply for a photon's energy?

    Higher energy. Energy directly proportional to frequency via $E = hf$.

21. Find the momentum of a photon with wavelength $\lambda = 700 \text{ nm}$.

    $p = \frac{h}{\lambda}$. Use momentum formula with given wavelength value.

22. What is the significance of the double-slit experiment?

    Demonstrates wave-particle duality. Shows particles behave as both waves and particles.

23. Which constant is used to describe quantization of energy?

    Planck's constant, $h$. Fundamental constant in energy quantization formulas.

24. What is the relation between frequency $f$ and wavelength $\lambda$?

    $c = f\lambda$. Speed of light equals frequency times wavelength.

25. What is the dual nature of light?

    Wave and particle. Light exhibits both wave and particle characteristics.

26. Find the de Broglie wavelength of an electron with momentum $p$.

    $\lambda = \frac{h}{p}$. Matter wavelength formula using momentum.

27. What principle limits simultaneous knowledge of position and momentum?

    Heisenberg uncertainty principle. Fundamental limit on measurement precision in quantum mechanics.

28. What is the equation for the energy of a photon in terms of wavelength?

    $E = \frac{hc}{\lambda}$. Combines speed of light with Planck's constant and wavelength.

29. What is the symbol $\hbar$?

    Reduced Planck's constant, $\hbar = \frac{h}{2\pi}$. Appears in angular momentum and uncertainty relations.

30. Calculate de Broglie wavelength for $p = 2 \times 10^{-27} \text{ kg m/s}$.

    $\lambda = \frac{h}{p}$. Apply de Broglie formula with given momentum value.

31. What is the significance of Planck's constant?

    Relates energy and frequency. Quantum of action linking energy and frequency.

32. How do you calculate the energy of a photon given its frequency?

    $E = hf$. Direct application of Planck's energy-frequency relation.

33. Which equation represents the photoelectric effect?

    $KE = hf - \phi$. Kinetic energy equals incident photon energy minus work function.

34. What did de Broglie propose about matter?

    Matter has wave properties. All matter exhibits wavelike behavior.

35. What is Heisenberg's uncertainty relation in terms of position and momentum?

    $\Delta x \Delta p \geq \frac{\hbar}{2}$. Fundamental quantum limit on simultaneous measurements.

36. Identify the formula for energy of a photon.

    $E = hf$. Directly proportional relationship between photon energy and frequency.

37. What is the principle behind quantum mechanics?

    Wave-particle duality. Core concept underlying all quantum mechanical phenomena.

38. How does increasing frequency affect photon energy?

    Photon energy increases with frequency. Direct proportionality from $E = hf$ relationship.

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