1 Quiz 7: 9am +q I2I2 I1I1 I3I3

Physics 7C Fa 2008 Quantum Mechanics Light as a particle Energy of light Energy levels in atoms

3 Outline Quiz Introduction to quantum mechanics Extremely brief overview of major models in the course (will be posted online if we don’t reach it) Final Exam Logistics Course reviews

4 Quiz 7: 7:30am +q I3I3 I1I1 I2I2

5 Quantum Mechanics Model It can be non-intuitive We can make sense of it using two models: Particle Wave

6 Quantum Mechanics Model Light and matter both behave like waves sometimes and like particles other times Confining waves to an area leads to standing wave patterns For bound matter, this results in only certain available energy levels Bound matter can gain or lose energy only between the available levels To conserve energy, usually a photon is absorbed or emitted with the correct energy (frequency)

7 Experimental Evidence: Photons Electrons in metal: Free to move Bound to metal Think of as binding energy Goal: free from metal Shine light to add energy. How can we get high energy light?! Laser Metal v

8 Experimental Evidence: Photons Binding Energy KE elec Light Energy Laser Metal v

9 Energy: Wave Model What makes a high energy wave? a)Big wavelength b)Big amplitude c)High wave speed In light, what would this look like? What do we observe if we increase the energy as the wave model suggests?

10 Energy: Wave Model High energy wave Large amplitude Large amplitude means more intensity More intensity means brighter Result of increasing brightness: If electrons were not freed at low brightness, they are also not freed at high brightness If electrons were freed at low brightness: Maximum energy at high brightness is unchanged More electrons are freed

11 Energy: Photon Model Changing color of light: If red light does not free electrons, sometimes other colors will If purple light does not free electrons, no visible light will. Color (frequency) of light is related to the energy! E = hf = energy of one photon h: Plank’s Constant =  Js Increasing intensity corresponds to increasing number of photons.

12 Which type of EM radiation is highest energy? a) Radiob) Visible c) X-ray

13 Quantum Mechanics: Light As a wave As a particle: E=hf Matter As a wave: =h/p As a particle: as you have always studied!

14 Quantum Mechanics Consequences of wave nature of matter 2-slit interference occurs for particles Confining a particle leads to standing waves Different standing waves have different wavelengths Different wavelengths correspond to different momenta Different momenta correspond to different energies All these things are quantized: only certain values are allowed

15 Atoms: electrons bound to nucleus Molecules: can model bonds as springs, with atoms bound together Examples of bound particles N N

16 Example of energy levels: Emission Spectra Add energy to an element and wait. Each element emits light of certain colors. Why? Hydrogen Helium Iron

17 Emission Spectra Each of the three marked transitions correspond to visible light. Which one is responsible for the red photon? E1E1 E2E2 E3E3 E4E4 E5E5 a b c

18 The three previous transitions corresponded to visible light. What part of the spectrum might the bold arrow correspond to? a)Green light b)Infrared (IR) c)Ultraviolet d)Microwave e)Gamma ray Emission Spectra E1E1 E2E2 E3E3 E4E4 E5E5

19 The three previous transitions corresponded to visible light. What part of the spectrum might the bold arrow correspond to? a)Green light b)Infrared (IR) c)Ultraviolet d)Microwave e)Gamma ray (way too high E) Answers to previous 2 Qs E1E1 E2E2 E3E3 E4E4 E5E5 Lowest  E makes red photon

20 Vibrational States: An example of discrete energy The images show energy levels for two different molecules. Which molecule can emit the longest wavelength photon, and why? 1)A: biggest ground state 2)A: highest spacing 3)C: goes up to E 6 4)C: lowest ground state 5)C: smallest spacing 6)Equal: constant spacing 7)Either: both can emit photons with arbitrarily long wavelengths. E1E1 E1E1 E2E2 E2E2 E3E3 E3E3 E4E4 E4E4 E5E5 E6E6 A C

21 Vibrational States: An example of discrete energy The images show energy levels for two different molecules. Which molecule can emit the shortest wavelength photon, and why? 1)A: biggest ground state 2)A: highest spacing 3)C: goes up to E 6 4)C: lowest ground state 5)C: smallest spacing 6)Equal: constant spacing 7)Either: both can emit photons with arbitrarily short wavelengths. E1E1 E1E1 E2E2 E2E2 E3E3 E3E3 E4E4 E4E4 E5E5 E6E6 A C

22 Answers to previous 2 Qs Which molecule can emit the shortest wavelength photon, and why? (7) The longest ? (4) E1E1 E1E1 E2E2 E2E2 E3E3 E3E3 E4E4 E4E4 E5E5 E6E6 A C 4)C: smallest spacing (longest corresponds to lowest energy. We are looking for the closest together levels.) 7)Either: both can emit photons with arbitrarily short wavelengths. (shortest corresponds to highest energy. These levels continue to arbitrarily high values, so dropping from an incredibly high level to the ground level will produce a very short wavelength photon.

23 Fluorescence Observe. You will discuss more in DL

24 Main Models Wave Model Ray Model Field Model (Electricity & Magnetism) Quantum Mechanics

25 Wave Model Waves in 1, 2, and 3 dimensions Interference 1D: pathlength & phase 2D: double slit Frequency dependent: Beats Standing Waves

26 Ray Model Rays perpendicular to wavefronts Rays do not interact (i.e. no interference) Optics Reflection Refraction Lenses (converging, diverging) Ray Tracing & Thin Lens Equations

27 Field Model Something (source) creates a field Field has magnitude at all points Field has direction at all points The net field is the vector sum of all source fields Something else (test) interacts with the field resulting in a force Force has magnitude we can determine Force has a direction we can determine Gravitation, Electricity, Magnetism

28 Final Exam Review sessions: probably Friday, Monday, Tuesday. Maybe some on the weekend. Check webpage for details! Exam: When: Wednesday 3:30-5:30 Where: Giedt 1001 & Giedt 1003 Check webpage for details! Questions?