Lecture 4

1. Lecture 4 Understanding Electromagnetic Radiation 1.5-1.7 30-Aug Assigned HW 1.1, 1.16, 1.20 1.21, 1.22, 1.23, 1.24, 1.33, 1.36 Due: Monday 6-Sept

2. Review 1.2-1.4 • Waves transmit energy • Electromagnetic Radiation • Electric Field • Magnetic Field • The visible spectrum is a VERY small part of the EM spectrum • Sunlight is considered a continuous spectrum • Contains many wavelengths • Sodium and Hydrogen emission spectra are both examples of discontinuous • Hydrogen spectrum • Balmer Series  visible • Lyman series  UV • Classical Physics cannot explain these observations • Blackbody Radiation • Stefan-Boltzmann and Wien’s laws • Quantum Theory – Discreet energy levels

3. Emission Lines and Energy Levels • We add energy (heat) to an element • ‘Excited’ electron • When the energy source is removed • Relaxes to ground state (n=1) • What happens when the energy added is more than the n=1  n=∞ transition?

4. Photoelectric Effect – the QT test • When light (hν) strikes a metal surface, electrons are ejected • Emission ONLY occurs when the incident light exceeds a threshold (φ) • The number of electrons emitted depends on the intensity of the incident light. • The kinetic energies of emitted electrons depend on the frequency of the light. Energy of Incident light Kinetic Energy Of ejected Electron Energy Required For Ejection Video

5. Photoelectric Effect – the QT test Example: The wavelength of light needed to eject an electron from hydrogen is 91.2 nm. Calculate the velocity of the particle ejected when 80.0 nm light is shone on a sample of hydrogen.

6. Photoelectric Effect – multiple samples These experiments verify that for each element, discreet amounts of energy are required to eject an electron, φ, which corresponds to a difference between two well defined energy levels

7. How Do We Find the Work Function? • Calculate the work function for a hydrogen atom.

8. Particle-like Properties of Photons • What have we talked about that suggests that electromagnetic radiation behaves very much like particles? Photon Hint: Requires a physical interaction between the photon and another particle This other particle is released with a specific hν

9. Wave-like Properties of Photons • Several observations indicate that photons have intrinsic wave-like properties • Dispersion through a spectrum

10. Wave-like Properties of Photons • Additional evidence of wave-like properties comes from observing the diffraction patterns of photons

11. Diffraction and Interference • When two waves traveling along different paths interact, they combine in an additive way. We call this interference. • Constructive Interference - • Destructive Interference –

12. Diffraction and Interference • Let’s revisit the diffraction patterns: • Where is the constructive interference? • Destructive?

13. Other uses of Diffraction • Solving the structure of proteins! • Dr. Hurlbert research

14. Particle-Wave Duality of Photons • Photoelectric Effect tells us that photons act like particles while diffraction and dispersion indicate wave-like properties • We conclude that a photon can take on characteristics of BOTH • Louis de Broglie suggested that all particles should have wavelike properties (‘matter-wave’) Linear momentum (kg m s-1) 1937 Nobel Prize was awarded for this discovery

15. Repercussions of Particle-Wave Duality • Classical Physics  • BUT…if a particle is really a wave, can we know where it is?

16. Repercussions of Particle-Wave Duality • Model of the atom….electrons • Classical physics predicts a trajectory with known ρ and x. • Particle-wave duality tells us this is NOT the case Classical Interpretation Quantum Mechanical Interpretation

17. Repercussions: Heisenburg Uncertainty • Niels Bohr and Werner Heisenberg investigated just how precisely we can determine the behavior of subatomic particles. • Two variable MUST be measured for a full understanding • ρ • x • They concluded that there must always be uncertainties in the measurement

18. Heisenburg Uncertainty Principle • When the position of the particle is well defined, the momentum is not • If the momentum is accurately known, the position is not

19. Using the Principle • An electron is traveling at 2.05 ± 0.03 x 106 ms-1. With what precision can we simultaneously measure the position of the electron?

20. Wavefunctions and Schrödinger • We need to adjust the mathematical definition of matter to account for particle-wave duality. • Edwin Schrödinger’s approach was to replace the trajectory of a particle with a wavefunction, ψ. • A wavefunction is: Yes, I rock the bowtie like a champ! Schrödinger also had a cat.

21. Wavefunctions and Probability • Physical usefulness of ψ came from Max Born • The Born interpretation states that: Probability density Why is this value never negative? What would a negative value indicate?

22. Wavefunctions and Probability Wake up and insert answer • Ψ2 is a density – dependent on • How do we calculate mass from density? ρ=m/V • Same for ψ2 Example: If ψ2 = 0.5 pm-3, calculate the probability of finding a particle in a sphere with a radius of 1pm.

23. Schrödinger’s Great Contribution which is often expressed as but what does this mean?

24. Particle in a Box • Imagine a particle confined to a box with a length of L. • Wavelengths are restricted to those with nodes at 0 and L. Why?

25. Particle in a Box • How do we find the energy of the particle? Allowed wavelengths are:

26. Quantization of Energy • We’ve established that for a particle in a 2D box. • Only certain wavelengths fit into the box, n is restricted to integers. • What does this tell us about the levels of energy? • Think about the Photoelectric Effect. Does this make sense?

27. Changing the Box Length • If we confine the particle to a smaller or larger space. What influence will it have on the energy levels? • Qualitatively  • Quantitavely  5 nm box vs. 500 nm box. Calculate n = 1 and n = 2.

28. Changing the Box Length • If we confine the particle to a smaller or larger space. What influence will it have on the energy levels?

29. What do the Energy Levels Mean?

30. Sample Problems • Use the particle-in-a-box model to calculate the wavelength of the third quanta of a box with a length of 100pm.

31. Sample Problems • Calculate the probability density for the particle in a box model. Much easier than it looks, isn’t it?

32. Sample Problems • Derive an equation that allows the difference between two energy levels to be determined.