Chapter 4, Part 5 PDF - Atomic Structure

TOPHAT - QUIZ TIME! Which of the following statements describes a node (There may be more than one answer). (a) A location at which there is zero probability of locating an electron. (b) A result of the wavefunction changing sign (+ to — or — to +) (c) A result of the probability density changing...

TOPHAT - QUIZ TIME! Which of the following statements describes a node (There may be more than one answer). (a) A location at which there is zero probability of locating an electron. (b) A result of the wavefunction changing sign (+ to — or — to +) (c) A result of the probability density changing sign (+ to — or — to +) (d) A node can be either angular or radial (e) The above statements all accurately describe nodes. TOPHAT - QUIZ TIME! What is meant by the term “shielding”? (a) Electrons can never penetrate the nucleus (b) Electrons in higher energy levels cannot feel the full charge of the nucleus (c) Gaseous atoms are repelled from each other by their electrons (d) Higher energy electrons penetrate through lower energy orbitals (e) None of the above ORBITALS – A SUMMARY  Electron orbitals can be described by three quantum numbers: (n, ℓ, 𝑚ℓ )  n = principal quantum number (n ≥ 1) → energy & size  ℓ = angular momentum quantum number (0 ≤ ℓ ≤ n – 1) → shape  𝑚ℓ = magnetic quantum number (−ℓ ≤ 𝑚ℓ ≤ ℓ) → spatial orientation  Orbitals contain nodes, regions where there is 0 probability of finding an electron  Any orbital contains n – 1 total nodes  Of those, the number of angular nodes is equal to ℓ  The remainder (𝑛 − ℓ − 1) are radial nodes  LET’S PRACTICE! Name the n and ℓ designation for the highlighted orbitals. Identify the number of angular and radial nodes for each. YOU SPIN ME ROUND LIKE A RECORD – ELECTRON SPIN QUANTUM #  Electron “spin”, ms, refers to the intrinsic angular momentum of all electrons. If “clockwise”, its spin is +1/2. If “counterclockwise”, its spin is –1/2.  This spin generates a very tiny magnetic field  If electrons are paired in an orbital, the orbital has no net magnetic field  The Stern-Gerlach experiment involved sending a beam of gaseous Ag atoms through a strong magnetic field  Electrically neutral but has 47 electrons. One of them must be unpaired!  The beam was deflected to two different spots  This proved that an electron’s angular momentum was quantized as well! INFLUENCE OF QUANTUM MECHANICS  Recall that quantum mechanics was designed to understand the behavior of electrons  Wave-particle duality → wave behavior manifests as orbitals  Orbitals are regions of high probability of locating an electron with a given energy  The location and energy of electrons in an atom dictate its chemical properties  The periodic table is arranged such that elements that share chemical properties are grouped together  Quantum mechanics explains electronic structure → chemical properties Structure determines properties ELECTRON CONFIGURATIONS  Atoms can take on a nearly infinite number of different electron configurations; however, no two elements share the same “ground state” configuration  Ground state: lowest energy  Configurations follow the generic form of: nℓ#  Each orbital can hold exactly 2 electrons  s(1) = 2, p(3) = 6, d(5) = 10, f(7) = 14  If two electrons occupy the same orbital, they must have opposite “spins”  The 4th quantum number, 𝑚𝑠 PAULI EXCLUSION PRINCIPLE  Sending gaseous atoms that have an even number of electrons through a magnetic field results in no splitting.  There must be the same number of “spin up” and “spin down” electrons  If you attempt to solve the wavefunction of an orbital containing two electrons with the same 𝑚𝑠 value, it collapses to 0!  Pauli summarized this in his exclusion principle: no two electrons in the same atom may have the same four quantum numbers  All electrons have a unique “address” FIGURE IT OUT! How many total electrons can occupy the 3rd energy level (n = 3)? (a) 8 (b) 10 (c) 18 (d) 24 (e) 32 SUBLEVEL ENERGY SPLITTING  Recall that the Rydberg equation only depends on the principal quantum number, n  All orbitals within a principal level of hydrogen are degenerate  When adding in more electrons, the wavefunction becomes unsolvable (at least analytically)  An additional consequence is that the orbital sublevels lose their degeneracy  In general, within the same principal level, E(s) < E(p) < E(d) < E(f)  Can be attributed to three factors  Coulomb’s Law  Charge Shielding  Wavefunction Penetration ATTRACTION AND REPULSION  Coulomb’s Law refers to the attraction/repulsion felt between two charged particles 1 𝑞1 𝑞2 𝐸= 4𝜋𝜖0 𝑑  An electron feels an attraction to the positively-charged nucleus  The more protons (higher Z), the stronger the attraction  An electron feels a repulsion to other electrons  An atom in the ground state will always try to minimize the potential CHARGE SHIELDING  Because of the repulsion of other electrons, an electron will not “feel” the full attraction towards the nucleus.  Zeff = effective nuclear charge  Net charge felt by an electron due to shielding FOR NEXT TIME… Read: The rest of 4.7