From Classical to Quantum: Understanding Atoms' Electronic Structure & Quantum Theory - Pr, Study notes of Chemistry

Download From Classical to Quantum: Understanding Atoms' Electronic Structure & Quantum Theory - Pr and more Study notes Chemistry in PDF only on Docsity! Quantum Theory and the Electronic Structure of Atoms Chapter 6 Our world until the end of the nineteenth century The Macroscopic World classical theory of electromagnetic Radiation by Maxwell Matter Radiation (Light) Newtonian Mechanics (Newton’s laws), Thermodynamics Studied and characterized by Classical Physics • The number of waves passing a given point per unit of time is the frequency (). • For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency. Electromagnetic Radiation • All electromagnetic radiation travels at the same velocity • the speed of light (c), 3.0  108 m/s. • Therefore, c =  The Nature of Energy of Radiation • The wave nature of light does not explain how an object can glow when its temperature increases. • Max Planck explained it by assuming that energy comes in packets called quanta. Another mystery involved the emission spectra observed from energy emitted by atoms and molecules. VIS 40 % IR 51 % UV 9 % nm 500 1000 nm 500max  Solar radiation intensity The Nature of Energy of Radiation Atomic spectra: http://astro.u-strasbg.fr/~koppen/discharge/index.html Demo: H, He, and Ne atoms Only a line spectrum of discrete wavelengths is observed. Emission Spectrum of the Hydrogen Atom Quantization of Energy of Electrons Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: 1. Electrons in an atom can only occupy certain orbits (corresponding to certain energies). 1. Electrons in an atom can only occupy certain orbits (corresponding to certain energies). 2. Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom. Bohr Model for the energy Levels of the hydrogen atom 2 H n n R E  1- 18 H cm 737,109 J 1018.2R    ,....3,2,1n n 1 2 3 4 5 n HR 4 RH 9 RH 16 RH 0 absorption emission a. What is the value of of an electron traveling at 1.00% of the speed of light? b. What is the value of of a person (m = 62.6 kg) moving at 1m/s? Let us carry out the following exercises mvP ; p h  Answer This wavelength is about five times greater than the radius of the H atom  A 43.2 103)kg(101.9 s.J10626.6 631 34       a.  A 1006.1 25 This wavelength is too small to be detectedb. a. Electron diffraction (Al) b. X-ray diffraction experiment (Al) http://www.matter.org.uk/diffraction/introduction/ what_is_diffraction.htm de Broglie Waves Are Observed Experimentally http://jchemed.chem.wisc.edu/JCEWWW/Articles/WavePacket/WavePacket.html   2 h ; 2 P.x   The Heisenberg Uncertainty Principle 2 )mv(.x   or In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself! Quantum Numbers • Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies. • Each orbital describes a spatial distribution of electron density. • An orbital is described by a set of three quantum numbers. Principal Quantum Number, n • The principal quantum number, n, describes the energy level on which the orbital resides. • The values of n are integers ≥ 0. Azimuthal Quantum Number, l • This quantum number defines the shape of the orbital. • Allowed values of l are integers ranging from 0 to n − 1. • We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals. Magnetic Quantum Number, ml • Orbitals with the same value of n form a shell. • Different orbital types within a shell are subshells. s Orbitals Spherical in shape. Radius of sphere increases with increasing value of n. l = 0 ml = 0 s Orbitals Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n−1 nodes, or regions where there is 0 probability of finding an electron. Energies of Orbitals • For a one-electron hydrogen atom, orbitals on the same energy level have the same energy. • That is, they are degenerate. Energies of Orbitals • As the number of electrons increases, though, so does the repulsion between them. • Therefore, in many- electron atoms, orbitals on the same energy level are no longer degenerate. Spin Quantum Number, ms • In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy. • The “spin” of an electron describes its magnetic field, which affects its energy. Electron Configurations Distribution of all electrons in an atom consist of 5p4 4 -Number denoting the energy level p -Letter denoting the type of orbital 5 -Superscript denoting the number of electrons in those orbitals Orbital Diagrams • Each box represents one orbital. • Half-arrows represent the electrons. • The direction of the arrow represents the spin of the electron. Some Anomalies Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row. For instance, the electron configuration for copper is [Ar] 4s1 3d5 rather than the expected [Ar] 4s2 3d4. These anomalies occur in f-block atoms, as well. This occurs because the 4s and 3d orbitals are very close in energy. 8O 11Na 19K Detailed and Abbreviated Electron Configurations Of Metals and Nonmetals 16S Detailed and Abbreviated Electron Configurations Of Transition Metals 21Sc 24Cr 25Mn 29Cu