Recall the Goal. What IS the structure of an atom? What are the properties of atoms?

Transcription

1 Recall the Goal What IS the structure of an atom? What are the properties of atoms? REMEMBER: structure affects function! Important questions: Where are the electrons? What is the energy of an electron? Chem 110 1

2 Review Quantized Energy Energy comes in discrete packets, or quanta Energy of a quantum ε is ε = hν ν = frequency of light h = Planck s constant = J s Total energy in light beam is nhν (n = 1, 2, 3, ) Dual Nature of Light Wave λν = c Particle E = hν Experimental support: black-body radiation (Planck, 1900) photoelectric effect (Einstein, 1905) line spectra of hydrogen (Bohr, 1913) Chem 110 2

3 Bohr Model of H atom (1913) Line spectrum is due to electronic transitions Atoms absorb or emit light when e changes its orbit E = E f E i = hν 1 1 h E RH 2 2 n i n f where n i and n f are integers. This predicts the H-atom spectrum EXACTLY! Note: n f > n i E is + (absorbs photon) n f < n i E is (emits photon) Chem 110 3

4 Energy levels in Bohr Model n = 6n = 5 n = 4 n=3 n = 2 Energy n = 1 Chem 110 4

5 Be able to use the Bohr Model to solve problems describing electronic transitions in the Hydrogen atom. If n i = 2 and n f = 1, is energy emitted or absorbed? 1. emitted 2. absorbed Of the following transitions in an H-atom, which one results in the emission of the highest energy photon? 1. n=1 n = 6 2. n=6 n = 3 3. n=3 n = 6 4. n=1 n = 4 5. n=6 n = 1 Chem 110 5

6 The Bohr model explained some experimental evidence for hydrogen atom, but it failed for other atoms. From Orbits to Orbitals : DeBroglie (1924): if light has dual wave/particle behavior, perhaps matter does also. Wavelength of matter waves: λ = h/mv Electron waves discovered in 1927 (Davidson and Garmer) (Basis for electron microscope) For a baseball and bacteria, λ is too small to observe, but for electrons λ is of atomic size producing profound effects. Electrons in atoms behave as "standing" waves. (Schrödinger equation, 1926) Enter the Quantum World Chem 110 6

7 There is experimental evidence for the wave behavior of electrons X-Ray diffraction electron diffraction Chem 110 7

8 Electron microscope provides experimental evidence that particles have wave properties. Electrons diffract when interacting with matter. Used to image some of the tiniest objects. Image of HIV budding from T-cell Chem 110 8

9 Heisenberg Uncertainty Principle It is NOT possible to simultaneously know the position & velocity (momentum, mv) of a particle with complete certainty Derives from wavelike nature of matter This really becomes important when dealing with subatomic matter All electrons have a velocity, therefore, you cannot specify their exact location Contradicts Bohr s planetary model of the hydrogen atom In other words: It is not appropriate to imagine e moving in nice little orbits around the nucleus Can we say anything about where the e are? Chem 110 9

10 Solutions of Schrödinger equation are wavefunctions (Ψ) H Ψ= E Ψ Ψ(x,y,z) yz) = wavefunction (no physical significance) Ψ 2 (x,y,z) = probability of finding one electron in a region of space, also called electron density Think of electrons as clouds of electron density. Orbitals = Ψ 2 (x,y,z) Chem

11 What is an orbital? Tells us WHERE the electron is Tells us the ENERGY of the electron An orbital obta specifies the probability of finding an electron in a given region of space, (i.e. orbitals have shapes) specifies the energy of the electron is characterized by quantum numbers (3 of them!) Chem

12 Classical waves have these characteristics Only certain stable modes are allowed Modes characterized by an integer (1 for each dimension) Nodes = points in wave where displacement is zero Equal (degenerate) νs appear in 2, 3 D due to symmetry. Standing waves are constrained We see similar characteristics in wavefunctions: Only certain modes (energy levels) are allowed. Modes are characterized by integers: Quantum numbers # nodes = n 1 Degenerate orbitals due to symmetry. Chem

13 In 3-D expect 3 quantum numbers n, and m 1. Principal quantum # (n) 1s 2s 3s Chem

14 Quantum numbers and nodes # of nodes is equal to n 1 Chem

15 The Quantum Number determines shape 2. Azimuthal quantum # ( ) Use symbols rather than numbers for = Chem

16 Quantum number m determines orientation 3. Magnetic quantum number (m ) Chem

17 Orbitals: Summary Allowed energy states for electrons in atom. Describes spatial distribution of electrons in these energy states. Orbital number shape name of orbitals? s 1 spherical p 3 dumbell d 5 clover leaf f 7?!?!? Quantum Numbers: defines n principal size azimuthal shape m magnetic orientation Chem

18 Orbital Energies Remember Orbital energy: is the energy needed to remove an electron from the orbital (positive) OR the energy released when an electron goes into an empty orbital (negative). Chem

19 ORBITAL ENERGIES: (BOHR MODEL) H atom: Energy does not depend on or m n = 6 n = 5 n = 4 n = 3 n = 2 Energy n = 1 Chem

20 What about the ORBITAL ENERGIES of other atoms? H He Chem

21 What about the ORBITAL ENERGIES of other atoms? RH Hydrogen: E 2 n 1 e atom with nuclear charge Z (He +, Li +2 ) : (still using BOHR MODEL) Multi-electron atom: What is Z eff? = effective nuclear charge Chem

22 Make This Your Own Chem

23 n 2 Shells, Subshells & Orbitals 2 = number of states t = number of orbitals in the n th shell. Subshells 1s # of orbitals 2s 2p 3s 3p 3d 4s 4p 4d 4f #orbitals in each subshell Chem

24 Shells, Subshells & Orbitals Shell: defined by Subshell: defined by quantum number quantum numbers Example: 3s (n = 3, = 0) 2p (n = 2, = 1) Orbitals of the same subshell have the same energy: they are degenerate Orbital: defined by quantum numbers Example: 2p x (n = 2, = 1) 2p y (n = 2, = 1) 2p z (n =2 2, =1) and m = 1, 0, 1 when = 1 Note: All of these have the SAME energy. Chem

25 By Wednesday You should have read Chapter 3 sections Complete Objective 2 in ALEKS (Dues Tues. Sept. 11) After Objective 2 you will be given a progress assessment in ALEKs. Before recitation on Thursday: complete Week 2 homework problems on pages 29 and 30. Chem