Quantum Physics Conceptual Questions, Quick Quizzes, and Problems

1. Chapter 27 Chapter 27 Quantum Physics Quantum Physics Conceptual questions: 1,3,9,10 Quick Quizzes: 1,2,3 Problems: 13,42,43,51

2. Problems which classical physics could not solve Problems which classical physics could not solve Blackbody Radiation Blackbody Radiation E&M radiation emitted by a heated object E&M radiation emitted by a heated object Photoelectric Effect Photoelectric Effect Emission of electrons by an illuminated metal Emission of electrons by an illuminated metal X-Ray Diffraction X-Ray Diffraction The Compton Effect The Compton Effect Spectral Lines Emitted by Atoms Spectral Lines Emitted by Atoms

3. Blackbody Radiation Blackbody Radiation An object at any temperature is known to emit electromagnetic radiation, called thermal radiation An object at any temperature is known to emit electromagnetic radiation, called thermal radiation Stefan’s Law, the power radiated by an object, P =  A e T 4 Stefan’s Law, the power radiated by an object, P =  A e T 4 T-temperature, A-area, e-emissivity,  =5.669 10 -8 W/m 2 K 4 T-temperature, A-area, e-emissivity,  =5.669 10 -8 W/m 2 K 4 The spectrum of the radiation depends on the temperature and properties of the object The spectrum of the radiation depends on the temperature and properties of the object

4. Blackbody Radiation Graph Blackbody Radiation Graph The wavelength of the peak of the blackbody distribution was found to follow Wein’s Displacement Law The wavelength of the peak of the blackbody distribution was found to follow Wein’s Displacement Law λ max T = 0.2898 x 10 -2 m • K λ max T = 0.2898 x 10 -2 m • K λ max is the wavelength at the curve’s peak λ max is the wavelength at the curve’s peak

5. The Ultraviolet Catastrophe and Planck’s theory The Ultraviolet Catastrophe and Planck’s theory Classical theory predicted infinite energy at low wavelengths Classical theory predicted infinite energy at low wavelengths Planck hypothesized that the blackbody radiation was produced by resonators Planck hypothesized that the blackbody radiation was produced by resonators The resonators could only have discrete energies The resonators could only have discrete energies E n = n h ƒ E n = n h ƒ n is called the quantum number n is called the quantum number ƒ is the frequency of vibration ƒ is the frequency of vibration h is Planck’s constant , 6.626 x 10 -34 J s h is Planck’s constant , 6.626 x 10 -34 J s

6. Photoelectric Effect Photoelectric Effect When light strikes E, photoelectrons are emitted When light strikes E, photoelectrons are emitted Electrons collected at C and passing through the ammeter are a current in the circuit Electrons collected at C and passing through the ammeter are a current in the circuit C is maintained at a positive potential by the power supply C is maintained at a positive potential by the power supply

7. Photoelectric Current/Voltage Graph Photoelectric Current/Voltage Graph Classical theory could Classical theory could not explain: not explain: The stopping potential is independent of the radiation intensity The stopping potential is independent of the radiation intensity The maximum kinetic energy of the photoelectrons is independent of the light intensity The maximum kinetic energy of the photoelectrons is independent of the light intensity The maximum kinetic energy of the photoelectrons increases with increasing light frequency The maximum kinetic energy of the photoelectrons increases with increasing light frequency

8. Einstein’s Explanation Einstein’s Explanation Light is a collection of photons (not waves) Light is a collection of photons (not waves) The photon’s energy would be E = h ƒ The photon’s energy would be E = h ƒ E=nhf-(n-1)hf E=nhf-(n-1)hf Each photon can give all its energy to an electron in the metal Each photon can give all its energy to an electron in the metal The maximum kinetic energy of the liberated photoelectron is KE = h ƒ – Φ The maximum kinetic energy of the liberated photoelectron is KE = h ƒ – Φ Φ is called the work function of the metal Φ is called the work function of the metal

9. Verification of Einstein’s Theory Verification of Einstein’s Theory Problem 27-13. What wavelength of light would have to fall on sodium (work function 2.46 eV) if it is to emit electrons with a maximum speed of 1.0 x 10 6 m/s?

10. Photocells Photocells Photocells are an application of the photoelectric effect Photocells are an application of the photoelectric effect When light of sufficiently high frequency falls on the cell, a current is produced When light of sufficiently high frequency falls on the cell, a current is produced Examples Examples Streetlights, garage door openers, elevators Streetlights, garage door openers, elevators

11. Problem 27-13 Problem 27-13 What wavelength of light would have to fall on sodium (with a work function of 2.46 eV) if it is to emit electrons with a maximum speed of 1.0 × 10 6 m/s? What wavelength of light would have to fall on sodium (with a work function of 2.46 eV) if it is to emit electrons with a maximum speed of 1.0 × 10 6 m/s?

12. X-Rays X-Rays Electromagnetic radiation with short wavelengths Electromagnetic radiation with short wavelengths Wavelengths less than for ultraviolet Wavelengths less than for ultraviolet Wavelengths are typically about 0.1 nm Wavelengths are typically about 0.1 nm X-rays have the ability to penetrate most materials with relative ease X-rays have the ability to penetrate most materials with relative ease Discovered and named by Roentgen in 1895 Discovered and named by Roentgen in 1895

13. Production of X-rays Production of X-rays

14. Schematic for X-ray Diffraction Schematic for X-ray Diffraction A continuous beam of X-rays is incident on the crystal A continuous beam of X-rays is incident on the crystal The diffracted radiation is very intense in certain directions The diffracted radiation is very intense in certain directions These directions correspond to constructive interference from waves reflected from the layers of the crystal These directions correspond to constructive interference from waves reflected from the layers of the crystal

15. Diffraction pattern for NaCl

16. Bragg’s Law Bragg’s Law Bragg’s Law gives the conditions for constructive interference Bragg’s Law gives the conditions for constructive interference 2 d sin θ = m λ m = 1, 2, 3… 2 d sin θ = m λ m = 1, 2, 3…

17. Compton Scattering Compton Scattering Compton assumed the photons acted like other particles in collisions Compton assumed the photons acted like other particles in collisions Energy and momentum were conserved Energy and momentum were conserved The shift in wavelength is The shift in wavelength is

18. QUICK QUIZ 27.1 An x-ray photon is scattered by an electron. The frequency of the scattered photon relative to that of the incident photon (a) increases, (b) decreases, (c) remains the same.

19. A photon of energy E 0 strikes a free electron, with the scattered photon of energy E moving in the direction opposite that of the incident photon. In this Compton effect interaction, the resulting kinetic energy of the electron is (a) E 0 , (b) E , (c) E 0  E , (d) E 0 + E , (e) none of the above. QUICK QUIZ 27.2

20. Photons and Electromagnetic Waves Photons and Electromagnetic Waves Light has a dual nature. It exhibits both wave and particle characteristics Light has a dual nature. It exhibits both wave and particle characteristics Applies to all electromagnetic radiation Applies to all electromagnetic radiation The photoelectric effect and Compton scattering offer evidence for the particle nature of light The photoelectric effect and Compton scattering offer evidence for the particle nature of light Interference and diffraction offer evidence of the wave nature of light Interference and diffraction offer evidence of the wave nature of light

21. Wave Properties of Particles Wave Properties of Particles In 1924, Louis de Broglie postulated that because photons have wave and particle characteristics, perhaps all forms of matter have both properties In 1924, Louis de Broglie postulated that because photons have wave and particle characteristics, perhaps all forms of matter have both properties Furthermore, the frequency and wavelength of matter waves can be determined Furthermore, the frequency and wavelength of matter waves can be determined

22. de Broglie Wavelength and Frequency de Broglie Wavelength and Frequency The de Broglie wavelength of a particle is The de Broglie wavelength of a particle is The frequency of matter waves is The frequency of matter waves is

23. A non-relativistic electron and a non- relativistic proton are moving and have the same de Broglie wavelength. Which of the following are also the same for the two particles: (a) speed, (b) kinetic energy, (c) momentum, (d) frequency? QUICK QUIZ 27.3

24. The Electron Microscope The Electron Microscope The electron microscope depends on the wave characteristics of electrons The electron microscope depends on the wave characteristics of electrons Microscopes can only resolve details that are slightly smaller than the wavelength of the radiation used to illuminate the object Microscopes can only resolve details that are slightly smaller than the wavelength of the radiation used to illuminate the object The electrons can be accelerated to high energies and have small wavelengths The electrons can be accelerated to high energies and have small wavelengths

25. The Uncertainty Principle The Uncertainty Principle When measurements are made, the experimenter is always faced with experimental uncertainties in the measurements When measurements are made, the experimenter is always faced with experimental uncertainties in the measurements Classical mechanics would allow for measurements with arbitrarily small uncertainties Classical mechanics would allow for measurements with arbitrarily small uncertainties Quantum mechanics predicts that a barrier to measurements with ultimately small uncertainties does exist Quantum mechanics predicts that a barrier to measurements with ultimately small uncertainties does exist

26. Heisenberg’s Uncertainty Principle Heisenberg’s Uncertainty Principle Mathematically, Mathematically, It is physically impossible to measure simultaneously the exact position and the exact linear momentum of a particle It is physically impossible to measure simultaneously the exact position and the exact linear momentum of a particle Another form of the principle deals with energy and time: Another form of the principle deals with energy and time:

27. Problem 27-43 Problem 27-43 In the ground state of hydrogen, the uncertainty of the position of the electron is roughly 0.10 nm. If the speed of the electron is on the order of the uncertainty in its speed, how fast is the electron moving? In the ground state of hydrogen, the uncertainty of the position of the electron is roughly 0.10 nm. If the speed of the electron is on the order of the uncertainty in its speed, how fast is the electron moving?

28. Thought Experiment – the Uncertainty Principle Thought Experiment – the Uncertainty Principle A thought experiment for viewing an electron with a powerful microscope In order to see the electron, at least one photon must bounce off it During this interaction, momentum is transferred from the photon to the electron Therefore, the light that allows you to accurately locate the electron changes the momentum of the electron

29. Scanning Tunneling Microscope (STM) Scanning Tunneling Microscope (STM) Allows highly detailed images with resolution comparable to the size of a single atom Allows highly detailed images with resolution comparable to the size of a single atom A conducting probe with a sharp tip is brought near the surface A conducting probe with a sharp tip is brought near the surface The electrons can “tunnel” across the barrier of empty space The electrons can “tunnel” across the barrier of empty space

30. Conceptual questions Conceptual questions 1. If you observe objects inside a very hot kiln, it is difficult to discern the shapes of the objects. Why? 1. If you observe objects inside a very hot kiln, it is difficult to discern the shapes of the objects. Why? 3. Are the blackbodies really black? 3. Are the blackbodies really black? 9. In the photoelectric effect, explain why the stopping potential depends on the frequency of the light but not on the intensity. 9. In the photoelectric effect, explain why the stopping potential depends on the frequency of the light but not on the intensity. 10. Which has more energy, a photon of ultraviolet radiation or a photon of yellow light? 10. Which has more energy, a photon of ultraviolet radiation or a photon of yellow light?

31. Problems Problems 42. A 50-g ball moves at 30.0 m/s. If its speed is measured to an accuracy of 0.10%, what is the minimum uncertainty in its position? 42. A 50-g ball moves at 30.0 m/s. If its speed is measured to an accuracy of 0.10%, what is the minimum uncertainty in its position? 51. Photons of wavelength 450 nm are incident on a metal. The most energetic electrons ejected from the metal are bent into a circular arc of radius 20.0 cm by a magnetic field with a magnitude of 2.00 × 10 –5 T. What is the work function of the metal? 51. Photons of wavelength 450 nm are incident on a metal. The most energetic electrons ejected from the metal are bent into a circular arc of radius 20.0 cm by a magnetic field with a magnitude of 2.00 × 10 –5 T. What is the work function of the metal?