Chapter 27 Quantum Theory

1. Chapter 27 Quantum Theory

2. Objectives • 27.1Describe the spectrum emitted by a hot body and explain the basic theory that underlies the emission of hot-body radiation • 27.1 Explain the photoelectric effect and recognize that quantum theory can explain it, whereas the wave theory cannot • 27.1 Explain the Compton effect and describe it in terms of the momentum and energy of the photon

3. Objectives • 27.1Describe the experiments that demonstrate the particle like properties of electromagnetic radiation • 27.2 Describe evidence of the wave nature of matter and solve problems relating wavelength to particle momentum • 27.2 Recognize the dual nature of both waves and particles and the importance of the Heisenberg uncertainty principle

4. Black Body Radiation • The hotter an object is • The more energy radiated away • The higher peak frequency emitted by the object • Every object emits electromagnetic waves • Result of vibrating particles and electrons falling down

7. Quantized Energy • The energy an atom has is quantized, meaning it can only have certain energies • Atoms in a solid can only vibrate at certain/specific frequencies • Energy is emitted when the atom changes its vibration • E = nhf • Where n is an integer, h is Planck’s constant, and f is frequency. 6.63x 10-34 • Energy = 2hf, or 3hf, or 4hf and so on

8. Quantized Energy • If an atom of energy 4hf were to change its energy to 3hf, it would emit radiation, equal to 1hf. • 5hf to 3hf would emit 2hf amount of energy • Going up requires receiving certain energies as well • These distinct packets of energy we call photons

9. Photoelectric Effect • The emission of electrons when EM radiation hits an object is known as the photoelectric effect

10. Photoelectric Effect • Not all radiation results in electrons given off. Need a minimum frequency, called the threshold frequency

11. Photoelectric Effect • Different materials have different threshold frequencies due to their differences in structure • Chem Connection • Ionization Energy • Electron Orbitals • Metals low • Non-metals high

12. Photoelectric Effect • If a red EM wave doesn’t ionize an object, 2red, 3red, or 1000red won’t either. • A bulb that produces more light doesn’t make it ionize • Need the right frequency

14. Common Uses of Photoelectric Effect • Garage door openers • Doors that open automatically for you when you get close

15. Photoelectric Effect • Threshold Frequency is the minimum amount of energy needed • What happens to the extra energy? • Turns into Kinetic Energy of the electron • KE = hf – hf0 • Kinetic Energy of electron equals the incident frequency minus the threshold frequency • Electrons can’t store energy, only get one photon (again, 2reds doesn’t help)

16. Photoelectric Effect • Not every electron in an atom requires the same amount of energy to escape. • Different subshells • They will leave with different amounts of KE

17. Electron Volt • Since electrons are small, and a joule is a very large unit, there is another way to discuss energy of an electron • The electron volt (eV) • 1 eV = 1.6 x 10-19 Joules • Same as electron charge for convience • This is how much energy an electron gets when it is accelerated across a 1.0 volt potential different

18. Electron Volt

19. Energy of an EM wave revisited • E = nhf rearranged for electron volts • E = (1240 eV * nm) / wavelength • How much energy (in eV) does a photon of wavelength 620 nm have?

20. Stopping Potential • How we determined the KE of electrons • Adjust Voltage until the electrons don’t make it

21. Simulator

22. Work Function • The threshold frequency is related to the energy needed to free the most weakly bound electron from a an object. This is called the work function • To find this energy, use • E = (1240 eV/nm) / wavelength

23. Questions • 1) The stopping potential for a photoelectric cell is 5.7 V. Calculate the KE of the emitted photoelectrons in eV. • The threshold wavelength of zinc is 310 nm • A) Find the threshold frequency of zinc • B) What is the work function in eV of zinc? • C) Zinc is illuminated by UV of 240 nm. What is the KE of the electron emitted?

24. Answered • 1) 5.7 eV is the KE of the emitted electrons • A) c / wavelength = frequency • Frequency = 9.7 x 1014 • B) 1240 / 310 = 4.0 eV • C) (1240 / 240) – (1240 / 310) = 1.2 eV

25. Compton Effect • Even though photon’s do NOT have mass*, they still have momentum • *Energy can be converted to mass technically • Momentum of a photon is equal to • Planck’s Constant Wavelength

28. What it all means • The initial photon transfers energy and momentum to the electrons. This transfer of momentum leads to a net loss of energy for the ejected photons (they have a longer wavelength)

29. Shifting to waves • The last ideas are evidence that photons are particles. We will now discuss wavelike properties of photons

30. de Broglie Wavelength • Since electrons diffract, de Broglie suggested they were also waves. • Since everything is made of electrons/protons, they should all have wavelike characteristics • Wavelength (de Broglie) = Planck’s Constant / Momentum of object

31. Wavelength of Baseball • Wavelength = 6.63 x 10-34 / (0.25 kg)(20m/s) = 1.3 x 10-34 • Too small to have an observable effect • What about an electron? • Its wave is large enough to be significant compared to itself

32. Question • An electron has a speed of 5.1 million m/s. What is its de Broglie Wavelength? • Momentum = Mass x Velocity • P = (9.11 x 10-31 kg)(5.1 million m/s) • h / p = wavelength • 6.63 x 10-34 / 4.6 x 10-24 • 0.14 nm

33. Where are you electron? • How do we see where an electron is (it’s location)? • By having a photon hit it. • But doesn’t the photon move the electron? • Yes, so if we know where it is, we have no idea where it is off too

34. Heisenberg Uncertainty Principle • The more certain you are of location, the less certain you are off the momentum