The Evolution of Matter: From Simple to Complex Prof. Jackson CC105 Music “Molecules” performed by Chick Corea Today’s Lecture • • • • Regularities in chemical properties The periodic table Connection to quantum mechanics Chemical bonds: – Ionic – Covalent • Molecules in space The Story of Stuff: So Far • The Big Bang made hydrogen and helium. • Stars made heavy elements and dispersed them through supernova explosions. • Gas clouds are filled with many different elements. General Principle: • At low temperatures, particles tend to prefer more binding energy and more bound particles • At high temperatures, particles tend to prefer more spatial freedom and more unbound particles. • In cold interstellar clouds, particles agglomerate into atoms and molecules. The Atom in Physics and Chemistry • Physics: electrons bound to a nucleus • Chemistry: smallest chemical unit Chemical Evidence for Atom • Compounds combine with small, whole number ratios of elements • These ratios represent the number of atoms that combine in each molecule of a compound: for example 2 H2 + O2 2 H2O • Atom: smallest unit to share in chemistry Crystals: Atoms packed together • Atoms combine in particular geometrical shapes Water Salt • Reflects the geometry of how individual atoms combine Crystals The Chemical Atom • Combines in specific ratios • Combines with particular geometric configurations The Periodic Table • Elements are arranged in columns according to chemical properties; rows according to atomic mass. • Successes – Organized elements in rational scheme – Predicted existence of new elements • Shortcoming – Empirical (how, not why) Periodic Table Evidence for the Physics Atom before Quantum Mechanics • Brownian motion---jiggles of small particles in a liquid can be explained by collisions with large numbers of atoms • Gas laws---relations between density, temperature, and pressure---can be explained by colliding atoms (or molecules) Physics vs. Chemistry How can physics account for the chemical properties of atoms? ? Quantum mechanics: connecting the physics and chemistry atom The Schrödinger Equation ħ2 2m 2 Ψ + VΨ = EΨ Application of Schrödinger Equation to Atom • Predicts wave function for electron orbiting nucleus (electric force) • Standing waves occur only for particular energies Orbitals Standing waves of probability The chance of finding an electron is given by the square of the wave function at a certain location Mathematical predictions from the Schrödinger equation Shapes of orbitals S Orbital Angular momentum = 0 Spherical Shapes of orbitals S Orbitals Can have several radial maxima Shapes of Orbitals P orbital Angular momentum = ħ Dumbbell 3 sets of p orbitals y y z z px x x x z y py pz Orbital Shapes: d orbitals D orbital Angular momentum = 2ћ Orbital Shapes: F orbitals F orbital Angular momentum = 3ћ Since they are waves, orbitals superpose y y x z y x z x z y y x x z P orbitals z P and S orbitals The Schrödinger Atom y x z The atom is a nucleus surrounded by a “cloud” of electron probability Comparison with the Bohr atom y x z Electrons in orbit around nucleus Probability waves in constructive interference How it all works • Orbitals have different energies • Orbitals have specific shapes • Electrons in a system settle into the lowest energy states available • Pauli Exclusion Principle Pauli Exclusion Principle No two electrons can have the same quantum state. Quantum state: a solution of the Schrödinger equation, which can be identified by its set of labels called “quantum numbers.” Quantum numbers represent (for electrons) l : Angular momentum = l x ħ (orbital motion) l = 0,1,2,3, … ml : Alignment of l along z-axis = ml x ħ ml = 0,+1,+2,+3,…. |ml| < l s : Intrinsic angular momentum (“Spin”) = s x ħ s=½ ms : Alignment of s along z-axis = ms x ħ ms = +½, -½ Quantized Projection of ℓ z l ml x y The projection of l along the z-axis, ml, is quantized, it can take only values 0,±1ћ, ±2ћ,…±nћ Only certain orientations for l are possible Orbital Angular Name momentum S 0 Number of possible l orientations 1 P ћ 3 D 2ћ 5 F 3ћ 7 “Spin” • No classical analogue • Intrinsic angular momentum s Two possible spin orientations Spin up ms = +1/2 Spin down ms = -1/2 Orbital Properties # of electron Orbital Angular states in Name Momentum orientations orbital #l S 0 1 2 P ħ 3 6 D 2ħ 5 10 F 3ħ 7 14 Principal Quantum Number n Number of nodes in standing wave rΨ n=1 r n=2 rΨ r rΨ n=3 r Nomenclature • nl –n = principle quantum number – l is called • S (l = 0) • P (l = 1) • D (l = 2) • F (l = 3) Example 2p Nomenclature • nl –n = principle quantum number – l is called • S (l = 0) • P (l = 1) • D (l = 2) • F (l = 3) Example 2p n=2, l=1 Larger n : Higher energy and larger size 1s orbital superposed on 2s orbital y x z Build Atom • Hydrogen 1 electron • Helium 2 electrons • Lithium 3 electrons Etc. … Electronic Configuration Nomenclature: nl# n principle quantum number l orbital angular momentum # number of electrons in orbital Open and Closed Shells • When all of the orbitals for a particular n (called a “shell”) are full, the shell is closed. • When the shell has empty slots, it is open. • Only electrons in open shells participate in chemistry. • Atoms with closed shells are chemically inert. Energy Level Diagram 3s 3px 3p 3pz y E 2s 2px 2p y 1s 2pz Energy Level Diagram 3rd shell 3s 3px 3p 3pz y E 2nd shell 2s 2px 2p y 1st shell 1s 2pz Energy Levels 3s 3px 3p 3pz y E 2s 2px 2p 2pz y Hydrogen 1s 1s1 Energy Levels 3s 3px 3p 3pz y E 2s 2px 2p y 1s Helium 1s2 2pz Energy Levels 3s 3px 3p 3pz y E 2s 2px 2p y Lithium 1s 1s22s1 2pz Energy Levels 3s 3px 3p 3pz y E 2s 2px 2p 2pz y Beryllium 1s 1s22s2 Energy Levels 3s 3px 3p 3pz y E 2s 2px 2p 2pz y Boron 1s 1s22s22p1 Energy Levels 3s 3px 3p 3pz y E 2s 2px 2p 2pz y Carbon 1s 1s22s22p2 Energy Levels 3s 3px 3p 3pz y E 2s 2px 2p 2pz y Nitrogen 1s 1s22s22p3 Energy Levels 3s 3px 3p 3pz y E 2s 2px 2p 2pz y Oxygen 1s 1s22s22p4 Energy Levels 3s 3px 3p 3pz y E 2s 2px 2p 2pz y Fluorine 1s 1s22s22p5 Energy Levels 3s 3px 3p 3pz y E 2s 2px 2p 2pz y Neon 1s 1s22s22p6 Energy Levels 3s 3px 3p 3pz y E 2s 2px 2p 2pz y Sodium 1s 1s22s22p63s1 Energy Levels 3s 3px 3p 3pz y E 2s 2px 2p 2pz y Magnesium 1s 1s22s22p63s2 Energy Levels 3s 3px 3p 3pz y E 2s 2px 2p 2pz y Aluminum 1s 1s22s22p63s23p1 Energy Levels 3s 3px 3p 3pz y E 2s 2px 2p 2pz y Silicon 1s 1s22s22p63s23p2 Energy Levels 3s 3px 3p 3pz y E 2s 2px 2p 2pz y Phosphorus 1s 1s22s22p63s23p3 Energy Levels 3s 3px 3p 3pz y E 2s 2px 2p 2pz y Sulfur 1s 1s22s22p63s23p4 Energy Levels 3s 3px 3p 3pz y E 2s 2px 2p 2pz y Chlorine 1s 1s22s22p63s23p5 Energy Levels 3s 3px 3p 3pz y E 2s 2px 2p 2pz y Argon 1s 1s22s22p63s23p6 Quantum Mechanics and the Periodic Table • All atoms with the same number of electrons in open shells have similar chemistry • Number of columns is due to the number of electrons allowed in orbitals Orbital Properties # of electron Orbital Angular states in Name Momentum orientations orbital #l S 0 1 2 P ħ 3 6 D 2ħ 5 10 F 3ħ 7 14 Periodic Table 2 1 s n 1 2 3 4 5 6 7 6 filled s2 p1 p2 p3 p4p5 10 d 14 f Chemical Bonds • Atoms tend to minimize their energy by obtaining a closed-shell configuration • Two possibilities – Lose or gain electrons (ion=charged atom) “Ionic bond” – Share electrons with other atoms “Covalent bond” Chemical Bonds: Ionic • Ions --- atoms that have gained or lost electrons beyond their neutral state • Positive ions’ charge balances negative ions • Shape of crystal results from packing together ions of different sizes Sizes of Ions Example: Salt = Sodium Chloride How do sodium and chlorine most easily obtain a closed-shell structure? Energy Levels 3s 3px 3p 3pz y E 2s 2px 2p 2pz y Sodium 1s 1s22s22p63s1 Energy Levels 3s 3px 3p 3pz y E 2s 2px 2p 2pz y Chlorine 1s 1s22s22p63s23p5 How does atom attain a closed shell? • Sodium has one extra electron, so it loses one. • Chlorine needs one extra electron, so it gains one. Example: Sodium Chloride + Sodium: loses electron Chlorine: gains electron Structure of Sodium Chloride • Ions pack together as closely as possible. • Forms cubic structure Cubic crystal results from atomic structure Other crystal structures Depends on sizes of ions Crystal forms Which atoms form ionic bonds? • Elements in first (second) column have one (two) loosely bound electron(s). • These atoms lose electrons and form positive ions. • Elements in last (next to last) column require one (two) electron(s) to complete a closed shell • These atoms lose electrons and form negative ions. Periodic Table + ++ Salts • Na (sodium) + Cl (chlorine) – Na+ + Cl- NaCl • Ba (barium) + F (fluorine) – Ba++ + 2F- BaF2 • Cs (cesium) + I (iodine) – Cs+ + I- CsI Chemical Bonds: Covalent The wave function of an electron from one atom overlaps that of an electron from a different atom Bonding orbital Constructive Interference + - + Negative charge screens one nucleus from the other, and attracts nucleus Anti-bonding orbital Destructive Interference + + Negative charge screen is absent, nuclei “see” each other, repel each other, attracted to negative charge opposite the nucleus Shapes of s Molecular Orbitals: Combine 2 s orbitals Molecular Orbitals Antibonding First electron unattached Second electron unattached Bonding Building Diatomic Molecules Anti-bonding 2s Bonding Hydrogen 2 bonding electrons 0 antibonding electrons Anti-bonding 1s Bonding H2 exists Anti-bonding 2s Bonding Helium 2 bonding electrons 2 antibonding electrons Anti-bonding 1s Bonding He2 does not exist Anti-bonding 2s Bonding Lithium 4 bonding electrons 2 antibonding electrons Anti-bonding 1s Li2 exists Bonding Anti-bonding 2s Bonding Beryllium 4 bonding electrons 4 antibonding electrons Anti-bonding 1s Bonding Be2 does not exist Diatomic Molecules • The following molecules have more bonding than anti-bonding electrons – H2, Li2, B2, C2, N2, O2, F2 – These molecules exist in nature • The following molecules have equal numbers of anti-bonding and bonding electrons – He2, Be2, Ne2, … – These do not exist in nature Larger Molecules: Water H H O Ice crystals Ice Crystals have hexagonal symmetry Larger Molecules Overlapping p orbitals Proteins Built up of 20 amino acids Green Fluorescent Protein Hemoglobin The shapes of biomolecules determines their function DNA Successes of Schrödinger Atom • Explains patterns in periodic table • Explains chemical properties of elements • Explains structure of crystals and molecules Molecules in the Interstellar Medium Molecules in Space • Supernova explosions enrich the interstellar gas with heavy elements • They become incorporated into gas clouds • Gas clouds can form molecules – Mostly H2 – But many, many other molecules are seen Molecular Lines in Interstellar Clouds Molecular Lines in Interstellar Clouds Interstellar Molecules Detected So Far Interstellar Molecules: Two Atoms AlF AlCl C2 CH CH+ CN CO CO+ CP CS CSi HCl HF H2 KCl NH NO NS NaCl OH PN SF SO S0+ SiN SiO SiS Carbon monoxide Hydroxyl radical Interstellar SiN Interstellar Molecules: Three Atoms C3 C2H C20 C2S CH2 HCN HCO HCO+ HCS+ HOC+ H20 H2S HNC HNO MgCN MgNC N2H+ N20 NaCN OCS S02 c-SiC2 CO2 NH2 H3+ SiCN Water! Interstellar Molecules: Four Atoms c-C3H l-C3H C3N C30 C3S C2H2 CH2D+? HCCN HCNH+ HNCO HNCS HOCO+ H2CO H2CN H2CS H30+ NH3 SiC3 Formaldehyde Ammonia Interstellar Molecules: Many Atoms CH3OH CH3C4H (CH3)20 CH3CH20H HC7N (CH3)2CO HC9N HC11N Alcohol! Interstellar Molecular Gas Clouds Interstellar gas clouds contain many complex, organic molecules. Presumably, these will be deposited onto the newly formed earth. Perhaps these molecules are responsible for the origin of life.