Wave Particle Duality – Light and Subatomic Particles

1. Wave Particle Duality – Light and Subatomic Particles • In high school physics light was treated as having both wave like and particle like character. Diffraction and refraction of light both exemplify its wave like properties. Particle like properties of light can also be demonstrated readily. One way to do this is to consider the photoelectric effect (see text) which implies, surprisingly, that light photons have momentum.

2. Subatomic Particles – Wave Character • A number of experiments show that small particles have observable wave like properties. Such wave like properties become increasingly important as one moves to particles of smaller mass. The electron is the most important of these particles. Interesting diffraction and refraction experiments have been conducted with electrons.

3. Mathematical Description of Electrons • The fact that electrons exhibit wave like behavior suggested that equations used to describe waves, and light waves in particular, might be modified to describe electrons. We will see some familiar mathematical functions used to describe the electron (e.g. cosθ, sin θ, eiθ). We will use so-called wave functions (Ψ’s) to gain insight into the behavior of electrons in atoms.

4. De Broglie’s Contribution • De Broglie used results/equations from classical physics to rationalize experimental results which proved that subatomic particles (and some atoms and molecules) had wave like properties. He proposed, in particular, that particles with a finite rest mass had a characteristic wave length – as do light waves.

5. 8-5 Two Ideas Leading to a New Quantum Mechanics • Wave-Particle Duality • Einstein suggested particle-like properties of light could explain the photoelectric effect. • Diffraction patterns suggest photons are wave-like. • deBroglie, 1924 • Small particles of matter may at times display wavelike properties. Louis de Broglie Nobel Prize 1918 General Chemistry: Chapter 8

6. Wave-Particle Duality E = mc2 h = mc2 h/c = mc = p p = h/λ λ = h/p = h/mu General Chemistry: Chapter 8

7. Wave properties of electrons demonstrated FIGURE 8-16 General Chemistry: Chapter 8

8. Probabalistic Description of Electrons • Classical physics suggests that we should be able (given enough information) to describe the behaviour of any body – changes in velocity, kinetic energy, potential energy and so on over time. Classical physics suggests that all energies are continuously variable – a result which very clearly is contradicted by experimental results for atoms and molecules (line spectra/quantized energies).

9. Uncertainty Principle • The quantum mechanical description used for atoms and molecules suggests that for some properties only a probabalistic description is possible. Heisenberg suggested that there is a fundamental limitation on our ability to determine precise values for atomic or molecular properties simultaneously. The mathematical statement of Heisenberg’s so-called Uncertainty Principle is given on the next slide.

10. The Uncertainty Principle h Δx Δp ≥ 4π Heisenberg and Bohr FIGURE 8-17 • The uncertainty principle interpreted graphically General Chemistry: Chapter 8

11. Atomic “Diagrams” • Many simple diagrams of atoms/atomic structure have limitations. In class we’ll consider some limitations of the C atom diagram shown on the next slide. • Representations of molecules are even more challenging – at least if we want to consider the electrons!

12. The “Carbon Atom” • Limitations?

13. A Molecular Model

14. Wave Functions and Standing Waves • If we wish to describe the behaviour of a system changing over time in three dimensional space we would need four variables - three coordinates and time. Classically, we might wish to describe the velocity of a satellite re-entering the Earth’s atmosphere and write, for example, v(x,y,z,t). General Chemistry: Chapter 8

15. Form of Wave Functions • For wave functions used to describe the behaviour of electrons in atoms we could, by analogy, write Ψ(x,y,z,t). For charged particles and Coulombic interactions, using spherical polar coordinates simplifies the mathematical work greatly. We then write wave functions as Ψ(r,ϴ,φ,t). It turns out that in many cases the properties of an electron, atom, or molecule do not change over time.

16. Wave Functions and Time • If the behaviour of an electron, atom or molecule does not change with time we can write simpler wave functions, such as Ψ(x,y,z) or Ψ(r,ϴ,φ). The classical analogy of a system with wave like behaviour not changing over time is any object that features standing waves. In such cases there is no destructive wave interference. Then wave like properties should be constant over time.

17. Standing Waves in Newtonian Mechanics • In macroscopic systems with “constant” wave like properties one sees nodes which do not move over time. An example would be a guitar string vibrating with, in the simplest case, two nodes occurring at each end of the string. More complex waves are possible for real systems – which again reflect constructive rather than destructive wave interference. Similar considerations apply to electrons.

18. 2L n Wave Mechanics • Standing waves. • Nodes do not undergo displacement. λ = , n = 1, 2, 3… FIGURE 8-18 • Standing waves in a string General Chemistry: Chapter 8

19. The electron as a matter wave FIGURE 8-19 General Chemistry: Chapter 8

20. Dihydrogen Oxide Waves

21. Sample Term Test 1 Example • B4. Consider the following reaction • 2 C(s) + O2(g) + 4 H2(g) 2 CH3OH(g)∆Hº = –402.4 kJ • [2] (a) Calculate a ΔUº value for the reaction at 25ºC. • [1] (b) How much heat would be released if 10.0 g of CH3OH(g) is formed from this reaction under constant volume conditions? • Reminder: The enthalpy change for the reaction as written gives the amount of heat released when two moles of gaseous methanol are formed at constant pressure. The internal energy change for the reaction as written gives the amount of heat released at constant V.

22. Sample Term Test 1 Example • [2] A5. A 16.0 L tank contains a mixture of helium gas at a partial pressure of 125.0 kPa and nitrogen gas at a partial pressure of 75.0 kPa. If neon gas is added to the tank, what must the partial pressure of neon be to reduce the mole fraction of nitrogen to 0.200?

23. Sample Term Test 1 Example • [4] B5. A sample of zinc metal reacts completely with an excess of hydrochloric acid: • Zn(s) + 2 HCl(aq) ZnCl2(aq) + H2(g) • The hydrogen gas produced is collected over water at 25.0ºC. The volume of the gas is 7.80 L, and the pressure is 0.980 atm. Calculate the amount of zinc metal in grams consumed in the reaction. (Vapor pressure of water at 25ºC = 23.8 mmHg.)