Chapter 8: Electrons in Atoms Or Quantum Mechanics Made Simple?

Transcription

1 1 Chapter 8: Electrons in Atoms Or Quantum Mechanics Made Simple? I. Introduction to Electronic Structure A. Interaction of Light and Matter 1. Properties of Light 2. Absorption and Emission of Light 3. The Bohr Model of the Atom II. Quantum Mechanics A. The H-atom 1. Atomic Orbitals and Quantum # s 2. Shapes of Orbitals B. Many Electron Atoms-Another Quantum # C. Electron Configurations and the Periodic Table

2 I. Introduction to Electronic Structure 2 A. Interaction of Light and Matter 1. Properties of Light (Electromagnetic Radiation)

3 Terms Used to Describe Waves How do we know light travels in waves? - it can be reflected, refracted, and diffracted 1. wavelength( ) distance between successive peaks (measured in nm for the light we do chemistry with) 3 2. frequency( ) number of wavelengths that pass a given point per unit time, measured in cycles per second, s -1 (Hz)

4 3. Amplitude maximum height of a wave (related to the intensity or brightness of the light, really the square of the amplitude) 4 Range of Wavelengths/Frequencies

5 5 Relationship Between λ, ν, and c Units wavelength usually given in nm, but must be converted to m for calculations Example #1 The light from red LEDs is commonly seen in many electronic devices. A typical LED produces 6.90x10 2 nm light. What is the frequency of this light? 6.90x10 c 2 c 2.998x10 8 nm m s 2 1m 6.90x10 nm 6.90x10 9 1x10 nm 8 m 2.998x10 c s x x10 m 7 m x10 s 14 Hz

6 6 Chemistry With Light UV Light Visible Light IR Light Microwaves

7 7 Energy of Light How much energy does light possess? Energy of Quantum of Light E =constant x frequency Constant = h = Planck s constant = x J-s Calculate Energy of a quantum of Light E = hν h = plancks constant

8 8 What is a Quantum of Light (Particle Nature of Light) Photoelectric effect the ejection of electrons from a metal surface when it is irradiated with UV radiation Observations of the Photoelectric Effect 1. no electrons ejected unless the radiation has a certain minimum energy (frequency) (each metal is different) 2. electrons are emitted immediately, regardless of the intensity of the radiation 3. K.E. of ejected electrons increases linearly with increasing frequency of radiation Einstein s Conclusions 1. Radiation striking metal surface behaves like a particle 2. Energy of photon = h radiation is quantized (same as that described by Planck)

9 Example Problem #2 Calculate the energy of one photon of UV light that has a wavelength of 280 nm. What is the energy contained in a mole of these photons? Is this enough energy to break a C-Cl bond in CCl3F (B.E. = 5.06x10-19 J)? (CFC years) nm 1m 280 nm 2.80x10 9 1x10 nm 7 m E hv hc x10 J s 2.998x10 m/ s x x10 m 19 J = 7.09x10-19 J Yes, it does have enough energy to break the C-Cl bond.

10 10 2. Absorption and Emission of Light (How do Matter and Light Interact?) What happens when atoms gain energy? What happens when atoms lose energy?

11 11 Terms Wavelength Spectrum Continuous Spectrum radiation separated into its components spectrum containing all wavelengths Line Spectra only certain wavelengths produced and separated Information from light emission

12 What is really going on? 12

13 13 3. Bohr Model of the Atom 1. Electrons move in circular orbits around the nucleus. 2. There are only certain allowed orbitals. 3. In order for an electron to move between orbitals it must gain/lose the right magnitude of energy. Absorption and Emission of Light from Atoms (Qualitative)

14 Good and Bad of the Bohr Model Good Electrons do reside in quantized orbitals, described by quantum numbers Energy is given off or absorbed when electrons move between energy levels Bad Doesn t work for multiple electron atoms Doesn t incorporate wave-like properties of electrons 14

15 15 II. Quantum Mechanics Matter and Waves De Broglie if radiation is particle-like and wave-like then perhaps all matter has both types of properties h mv Comparison Electron m = 9.11x10-31 kg v = 1x10 7 m/s = 7x10-11 m (7x10-2 nm) Baseball m = 0.10 kg v = 45 m/s (100 mph) = 1.5x10-34 m (1.5x10-25 nm) Uncertainty Principle - If matter travels in waves how do we know where it is? Uncertainty principle It is impossible to know the exact position and momentum (mv) of a particle

16 16 Uncertainty Principle Cont d Mathematically - x m v h 4 x = uncertainty in position mv = m v = mass times uncertainty in velocity Example Problem The electron has a mass of 9.11x10-31 kg. Assume we know the speed of the electron to be 5x10 6 m/s and this value has an uncertainty of 1%. What is the uncertainty in position of the electron? h h x m v x 4 4 m v 6 4 v.01 5x10 m / s 5x10 m/ s m 9.11x10-31 kg 2 34 m 6.63x10 kg s 2 x s 9 1x10 m x10 kg 5x10 m / s 2. Quantum Radius Mechanics of H-atom = 1x10-10 m

17 A. The H-atom 1. Atomic Orbitals and Quantum # s Schrödinger Wave Equation 1-dimensional 1 variable (1 quantum #) 2 2 d V ( x) E 2 2m dx 3-dimensional 3 variables (3 quantum # s) d d d V ( x, y, z) E m dx dy dz m = mass of particle ђ = planck s constant / 2 17 Orbital Me describes the regions in an atom where the probability of finding an electron is high (found by squaring the wave function) H-atom

18 18 Orbitals Atom - an apartment building for electrons S s Equation - provides 3 identifying properties that help us locate an electron Apt analogy Atom n l m l floor # of apt on # of rooms each floor in each apt distance shape of # of orbitals from space e- can of a specific nucleus occupy shape n

19 19 l Mention Name and Shape Value of l Letter s p d f g h

20 20 ml Representation of Some Orbitals For H n = 1 n =2 n = 3 l = 0 l = 0 l = 1 l = 0 l = 1 l = 2 1s 2s 2p 3s 3p 3d ml =