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Transcript
Lecture 20: Polyelectronic Atoms • Reading: Zumdahl 12.10-12.13 • Outline: – Spin (the 4th quantum number) – The Aufbau (“filling-up”) Principle – Filling up orbitals and the Periodic Table – Electronic Configuration (Core and Valence electrons) • Problems Chapter 12 Zumdahl 5th Ed. – 61-67, 71,72d, 75, 76, 78 1 Spin: The Fourth and final quantum number • Electrons have spin even when free in space; not part of an atom. • Further experiments demonstrated the need for one more quantum number. • Specifically, some particles (electrons in particular) demonstrated inherent (or internal) angular momentum. 2 Electron Spin Each and every electron has spin ½. (It is internal to the electron) Protons and neutrons also have spin ½. ms = 1/2 • The new quantum number is ms (analogous to ml). • For the electron, ms has two values: +1/2 and -1/2 ms = -1/2 • Half integer spin is an odd kind of angular momentum not shared by orbital angular momentum (Z12.65) No it does not really spin, but close. 3 The Aufbau Principle • For polyelectronic (i.e. real) atoms, a direct solution of the Schrodinger Equation is not possible. (Can’t solve the 3 body motion problem; Z12.61) • When we construct polyelectronic atoms, we use the hydrogen-atom orbital nomenclature to discuss in which orbitals the electrons reside. • This is an approximation (and it is surprising how well it actually works). This appx. implies effective nuclear charges to hold electrons when there are many electrons • Aufbau is German for “Building Up”. We are building a multielectronic atom from the rules for the 1 electron atom (so a few things get modified), but it works pretty well. 4 Pauli’s Principle for many electron atoms • When placing electrons into orbitals in the construction of polyelectronic atoms, we use the Aufbau Principle. (German for Up-Building) • This principle states that in addition to adding protons and neutrons to the nucleus, one simply adds electrons to the hydrogen-like atomic orbitals • Pauli exclusion principle: No two electrons may have the same (4) quantum numbers. Therefore, only two electrons can reside in an orbital (differentiated by ms). 5 First Row (Electronic Configuration) • Orbitals are filled starting from the lowest energy (to get the lowest total-energy atoms, called the ground state) • First number is the principle quantum number, letter is the angular quantum number. • Example: Hydrogen 1s1 1s 2s 2p • Example: Helium (Z = 2) Number of Electrons in the set of orbitals 2 1N s 1s 2s 2p E .C . 6 Second Row (E.C.) • Lithium (Z = 3) 1s22s1 1s 2s 2p • Berillium (Z = 4) 1s22s2 1s 2s 2p • Boron (Z = 5) 1s22s22p1 1s 2s 2p 7 Hund’s Rule • Carbon (Z = 6) 1s22s22p2 1s 2s 2p Hund’s Rule: Lowest energy configuration is the one in which the maximum number of unpaired electrons are distributed amongst a set of degenerate orbitals. • Nitrogen (Z = 7) 1s22s22p3 1s 2s 2p 8 Finish 2nd row (n=2) (E.C.) • Oxygen (Z = 8) 1s22s22p4 1s 2s 2p • Fluorine (Z = 9) 1s22s22p5 1s 2s 2p • Neon (Z = 10) 1s22s22p6 1s 2s 2p full 9 Third Row (n=3) Valence Electrons – the higher energy ones, used for chemistry Core electrons -- those of low energy that can be the set of electrons in the noble gas contained within the atom • Sodium (Z = 11) 1s22s22p63s1 Ne [Ne]3s1 3s • Argon (Z = 18) [Ne] 3s23p6 Ne 3s 3p 10 Summary: First 3 Rows We now have the orbital configurations for the first 18 elements. How did we know the order? Follow the periodic table. Why not 3d before we hit noble gasses? • Elements in same column have the same # of valence electrons! • For Main Group elements we are filling the p orbitals • For Alkali and Alkaline Earth elements fill the s orbitals. 11 Problems Z12.66-67 • Give the ground state: E.C. for Si, B, Al, S • Give the first excited state E.C. for B. 2 2 2 2 • An O atom has the E.C. 1s 2 s 2 px 2 p y – How many upaired electrons are present? – Is this an excited state for O? – In going from this state to the ground state would energy be released or absorbed, why? • Maximum number of electrons with these Q.N.s? – (in general the max number of electrons is 2 times the number of orbitals). n = 4 ⇒ 16 ⋅ 2 = 32 n = 5, ms = 12 ⇒ 25 ⋅1 n = 3, A = 3 ⇒ 7 ⋅ 2 = 14 n = 2, A = 1, mA = −1, ms = −21 ⇒ 1 12 Paramagnetism (Z12.75,78) • The number of unpaired electrons in an atom (either in ground state or an excited state) can be measured by a paramagnetism experiment. • The experiments provide us with indications of the E.C. of each atom. • Consider the ground state E.C. of Li, Ni, Ba, Hg: – Which is paramagnetic: Li, Ni. – How many unpaired electrons are expected. (1,2,0,0) • Is this an excited state E.C? 1s 2 2 s 2 2 p 4 3s1 – What neutral atom is it? (9 electrons, F) 2 2 5 0 – What is the ground state E.C? 1s 2 s 2 p 3s – How many unpaired electrons in the ground state and excited state? (1, and 3) 13 th 4 Row (E.C.) Similar to Sodium, we begin the next row of the periodic table by adding electrons to the 4s orbital. Order gets a bit confusing: we have inner and outer shell valence electrons • Why not 3d before 4s? • 3d is closer to the nucleus; think about electron crowding • 4s is energetically preferred, but the energetics are close, more on this later. 14 4th Row • Elements Z=19 and Z= 20: Z= 19, Potassium: 1s22s22p63s23p64s1 = [Ar]4s1 Z= 20, Calcium: 1s22s22p63s23p64s2 = [Ar]4s2 • Elements Z=21 to Z=30 have occupied d orbitals: Z= 21, Scandium: 1s22s22p63s23p64s23d1 = [Ar] 4s23d1 Z = 24, Chromium: [Ar] 4s13d5 Exceptions: Maximizes/Symmetrizes Unpairing Z12.71,72d Z= 29, Copper: 1s22s22p63s23p64s13d10 = [Ar] 4s13d10 Z= 30, Zinc: 1s22s22p63s23p64s23d10 = [Ar] 4s23d10 15 Periodic Table: The magic of 1,3,5,7 ← 2 ⋅1 → ← ← 2⋅5 ← 2⋅3 → → 2⋅7 → This orbital filling scheme gives rise to the modern periodic table. 16 Lanthanides • After Lanthanum ([Xe]6s25d1), we start filling 4f. 17 Actinides • After Actinium ([Rn]7s26d1), we start filling 5f. 18 Column Numbering • Heading on column given total number of valence electrons. 19 The Modern Periodic Table 20