1. ATOMIC STRUCTURE & PERIODICITY (Part 1; sec 1-8) Light, Matter Structure of the one-electron atom Quantum Mechanics

2. STRUCTURE OF ATOM (Pre-1900; Classical Science = CS) Electrons (-1 charge) and Protons (+1 charge) had been observed. Models of the Atom –“Raisin Pudding”: J.J. Thomson –Small positive nucleus surrounded by a lot of empty space through which the electrons are dispersed: Rutherford (1911) A third sub-atomic particle, the Neutron was discovered by Chadwick (1932)

3. LIGHT or EM RADIATION: WAVE CS considered electromagnetic radiation (EM) or light as a wave based on observations of diffraction, reflection, interference, refraction. Form of energy, delocalized, no mass Wavelength, λ = c/νm Frequency, ν Hz = 1/s Speed, c = λ ν 3.00E+08 m/s

4. Figure 7.1 The Nature of Waves

5. ELECTROMAGNETIC SPECTRUM Light or electromagnetic radiation spans many orders of magnitude in E, ν, and λ. Figure 7.2 Visible: ROY G. BIV400-800 nm At lower E and ν, λ increases: Infrared, microwave, radiowave At higher E and ν, λ decreases: Ultraviolet, X-rays, gamma-rays

6. ELECTRONS, PROTONS, NEUTRONS: PARTICLES CS considered these subatomic particles to be particles with mass (m), velocity (v) and momentum (mv) It was assumed that an object was either a wave (light) or a particle (electron).

7. FROM CLASSICAL TO QUANTUM THEORY From the late 1800’s to the 1920’s, many experimental observations that could not be explained by CS were recorded. These led to the development of Quantum Mechanics (QM) and a new structure of the atom. –A heated solid (blackbody) absorbs or emits quantized energy packets (not continuous packets), ΔE = nhν (n = integer) (Planck, 1900)

8. FROM CS TO QM (2) –Radiation is quantized and consists of particle waves called photons: photoelectric effect, E ph = hν = hc/λ (Einstein, 1905) –Particles have wave properties: electron diffraction –Atomic line spectra (Balmer,1885) As scientists worked to understand these and other exptal results, several conclusions emerged: –Electrons have WAVE and particle properties. –Light has PARTICLE and wave properties. –deBroglie Eqn expresses this: λ = h/mv; duality of nature

9. PHOTOELECTRIC EFFECT Expt: Shine light on clean metal surface and detect electrons ejected from metal. –Vary Energy (E = hν = hc/λ) and Intensity of light –Measure number (#) and kinetic energy of electrons (KE = 1/2 mv 2 ).

10. PHOTOELECTRIC EFFECT (2) Observations ( conflicted with CS) –Light must have a minimum energy value in order to eject electrons; this is called the threshold energy = hν o. (CS said no threshold energy exists). –If E ph > hν o, then # of electrons increased with the intensity of light. (CS said # electrons increased with frequency of light). –If E ph > hν o, then KE of electrons increased with the frequency of light. (CS said # electrons increased with intensity of light).

11. PHOTOELECTRIC EFFECT (3) Conclusions –Energy of photon = hν = hν o + 1/2 mv 2 if hν>hν o Conservation of energy statement. –If hν>hν o, then no electrons are ejected. –Energy of light = mc 2 means that light has “mass” (apparent mass, relativistic mass) m = E/c 2 = h/ λc –Light = wave AND particle (photon) with quantized energy

12. ATOMIC LINE SPECTRA CS: Rutherford model of the atom. Expt: When atoms are excited, they return to their stable states by emitting light. This light can be recorded to produce an atomic spectrum. Early experiments showed that the spectra consists of lines and that atoms from different elements gave different line spectra. Fig 7.6 What do these spectra tell us about the structure of the atom?

13. ATOMIC LINE SPECTRA (2) Balmer measured the emission spectrum of H and fit the observed wavelengths of the emitted light to an equation: ν = Rc (1/2 2 – 1/n 2 ) where R = Rydberg constant = 1.097E-2 1/nm The emission lines of the H atom in other regions of the EM spectrum fit the Balmer-Rydberg Eqn: ν = Rc (1/m 2 – 1/n 2 ) for n > m; n and m are integers or quantum numbers. (empirical eqn.) Each emission line is associated with an electron going from state n to state m.

14. Figure 7.7 A Change Between Two Discrete Energy Levels Emits a Photon of Light

15. BOHR ATOM (Fig 7.8) The Rutherford model could not explain these results, but Bohr’s “planetary” or quantum model could (1914). Bohr assumed quantized orbital angular momentum values such that when centrifugal force out (merry-go-round) = electrostatic attraction in, the electron was in a stable state. This model led to quantized electronic energy levels and to an eqn consistent with the Balmer-Rydberg Eqn. The energy of an electron in the nth energy level is quantized and equals E n = - hcRZ 2 /n 2 = -2.178E-18 Z 2 /n 2 J where n = 1, 2, 3...; note energies of bound states < 0

16. BOHR ATOM (2) Then when an electron goes from one quantized level (n) to another (m), light is emitted or absorbed. The energy of this light is ΔE = hc/ λ = hν = Rhc (1/m 2 – 1/n 2 ). (based on theory of atom) The wavelength of the light is 1/λ = R(1/m 2 -1/n 2 ) The Bohr atom is the basis for the modern theory of the atom but it has limitations. For example, it is only accurate for 1-electron atoms and ions.

17. Figure 7.8 Electronic Transitions in the Bohr Model for the Hydrogen Atom

18. QUANTUM MECHANICS (Schrodinger, 1926) The QM model of the atom replaced the Bohr model. This model is based on electron’s wave properties. The stable states of the electron in an atom are viewed as standing waves around the nucleus. (Fig 7.10) These standing waves (Ψ) are called wave functions and are interpreted as the allowed atomic orbitals for electrons in an atom.

19. Figure 7.10 The Hydrogen Electron Visualized as a Standing Wave Around the Nucleus

20. QUANTUM MECHANICS (2) The goal of QM is to solve the Schrodinger Eqn, H Ψ = E Ψ; i.e. find Ψ = atomic orbital plus the associated (quantized) energy for these stable states of the electron in the hydrogen atom. Ψ 2 is related to the probability of finding an electron at a particular (x,y,z) location. Ψ 2 is called the probability distribution. (Fig 7.11) Ψ 2 4πr 2 is the radial probability distribution (Fig 7.12); probability of finding electron at a particular r value and any angular values.

21. Figure 7.11 a&b (a) The Probability Distribution for the Hydrogen 1s (GROUND STATE) Orbital in Three- Dimensional Space (b) The Probability of Finding the H 1s Electron at Points Along a Line Drawn From the Nucleus Outward in Any Direction

22. Figure 7.12 a&b Cross Section of the Hydrogen 1s Orbital Probability Distribution Divided into Successive Thin Spherical Shells (b) The Radial Probability Distribution (max = a o = 5.29E-2 nm)

23. QUANTUM MECHANICS (3) Heisenberg Uncertainty Principle (1927) states that we cannot know the position and momentum of an electron (considered a wave) exactly. (vs CS) Δx Δ(mv) ≥ h/4 π Neither Δx nor Δ(mv) can be zero.

24. QUANTUM MECHANICS (4) The Ψ = wave function = orbital for a stable state of the electron. Each Ψ is defined by 3 quantum numbers that are related to each other; a set of Ψs lead to atomic electronic configurations. QM is the basis for understanding chemical bonding, molecular shapes (Chap.8 and 9), chem reactions, phys. and chem. properties.

25. ATOMIC ORBITALS AO) and QUANTUM NUMBERS (QN) Principal QN, n = 1, 2, 3…(K, L, M...shell); determines energy (quantized) and size of atomic orbital. Angular momentum QN, ℓ = 0, 1, 2…n-1 (s, p, d… subshell); determines shape of atomic orbital. For each n value, there are n ℓvalues. Fig 7.14-17)

26. Figure 7.13 Two Representations of the Hydrogen 1s, 2s, and 3s Orbitals (a) The Electron Probability Distribution (b) The Surface Contains 90% of the Total Electron Probability (the Size of the Oribital, by Definition)

27. Figure 7.14 a&b Representation of the 2p Orbitals (a) The Electron Probability Distribution for a 2p Oribtal (b) The Boundary Surface Representations of all Three 2p Orbitals

28. Figure 7.16 a&b Representation of the 3d Orbitals (a) Electron Density Plots of Selected 3d Orbitals (b) The Boundary Surfaces of All of the 3d Orbitals

29. Figure 7.17 Representation of the 4f Orbitals in Terms of Their Boundary Surfaces

30. AOs and QNs (2) Magnetic, m ℓ = - ℓ, …-2, -1, 0, +1, +2, …+ ℓ; determines spatial orientation of orbital. For each ℓ value, there are 2ℓ + 1 m ℓ values. Spin, m s = +1/2, -1/2; determines orientation of electron spin axis.

31. AOs and QNs (3) There are relationships (limitations) between four quantum numbers (Table 7.2) For the H atom and other one-electron atoms, all AOs with the same n value have the same energy. This is called energy degeneracy. (Fig 7.18)

32. Figure 7.18 Orbital Energy Levels for the Hydrogen Atom