C06-F09_DCD_D.pdfVIP

4:11 Principles of Chemistry ? Quantum-mechanical model for the H atom applies to many-electron atoms but some differences exist ? spatial structure of orbitals are similar ? electrons (orbitals) repel each other, which influences orbital energies ? In many-electron atoms, the electron-electron repulsion removes the orbital degeneracy observed within subshells (different l of same n) of the H atom (more details in Chapter 7) ? Within a shell (same n), the orbital energies of many- electron atoms increase as l increases: s p d f 7. Many-Electron Atoms Orbitals and their Energies ? degeneracy in n observed for the H atom is removed in many-electron atoms due to electron-electron repulsion ns np nd nf ? energy specified by n, l; the ml levels remain degenerate ? energies and relative ordering of orbitals varies from element to element Qualitative Orbital Energy Diagram For Many-Electron Atom Spin Quantum Number, ms ? The “spin” of an electron generates a magnetic field. ? The spin quantum number has only 2 allowed values: ms = +1/2 and –1/2 ? In the 1920s, it was discovered that a fourth quantum number was required to describe the H atom: the spin quantum number, ms 4:11 Principles of Chemistry Magnetic Resonance Imaging Nuclear “spin” Pauli Exclusion Principle Therefore, no orbital (Ψn,l,ml) may have more than 2 electrons, and they must have oppositely aligned spins. No two electrons in the same atom can have the same set of 4 quantum numbers. ! n, l, m l # $ n, l, m l , m s (±1/ 2) (orbital) 2 spin states (spin-orbitals) En, l (ml and ms degenerate) Quantum Number Values Number of Values Significance Principal, n 1, 2, 3, ... - distance from nucleus Angular, l 0, 1, 2, ..., n-1 n shape of orbital Magnetic, ml -l,...,0,...+ l 2l + 1 orientation of orbital Spin, ms - , + 2 direction of electron spin Allowed Quantum Numbers (Review) # orbitals in shell = n2 # electrons in shell = 2n2 # orbitals