Department of Chemistry and Biochemistry CHM Reeves CHM 101 – Chapter Six The Wave Nature of Light Quantized Energy and Photons Line Spectra and the Bohr Atom The Wave Behavior of Matter Quantum Mechanics and Atomic Orbitals Representations of Orbitals\ Many Electron Atoms Electronic Configurations Electronic Configurations and the Periodic Table

Department of Chemistry and Biochemistry CHM Reeves The Wave Nature of Light Electromagnetic radiation ranges from long wave length (low frequency) radio waves to short wave length (high frequency) gamma and cosmic rays.

Department of Chemistry and Biochemistry CHM Reeves The Wave Nature of Light A local radio station broadcasts at a frequency of 91.3 MHz. What is the wave length of the electromagnetic radiation on which this signal is broadcast? What is the frequency of red light that has a wave length of 650 nm?

Department of Chemistry and Biochemistry CHM Reeves Quantized Energy & Photons When an object is heated, it often glows. As the temperature rises, the color of the emitted light changes.

Department of Chemistry and Biochemistry CHM Reeves Quantized Energy & Photons To explain the spectral profile of black body radiation, Max Planck postulated that light’s energy (E) is proportional to its frequency ( ).

Department of Chemistry and Biochemistry CHM Reeves Quantized Energy & Photons Both the earth ( = 289K) and the sun ( = 5880K) are (imperfect) black body radiators.

Department of Chemistry and Biochemistry CHM Reeves Quantized Energy & Photons Einstein applied this idea to explain the photoelectric effect. When light with a frequency below a fundamental frequency ( < 0 ) irradiates the surface, no electrons are observed. When light of higher frequency ( > 0 ) irradiates the surface, electrons are observed instantly. Higher frequencies produce electrons with higher kinetic energies.

Department of Chemistry and Biochemistry CHM Reeves The Wave Nature of Light What is the energy of a photon with a frequency of 8x10 17 s -1 ? What is the energy of a mole of photons each with a wave length of 200 nm?

Department of Chemistry and Biochemistry CHM Reeves The Bohr Atom When visible light is directed through a prisim, a continuous spectrum of colors (frequencies) is observed.

Department of Chemistry and Biochemistry CHM Reeves When light emitted by excited atoms is directed through prisim, spectra consisting of lines at discrete wave lengths are observed. The Bohr Atom

Department of Chemistry and Biochemistry CHM Reeves When light emitted by excited atoms is directed through prisim, spectra consisting of lines at discrete wave lengths are observed. The Bohr Atom

Department of Chemistry and Biochemistry CHM Reeves Balmer observed that the wave lengths ( ) of the lines in this spectrum could be calculated using the equation: The Bohr Atom Where n 1 and n 2 are integers, and n 2 > n 1, and R H is the Rydberg Constant (1.10x10 7 m -1, 2.18x J). Although this equation predicts every line observed in the hydrogen emission spectrum, scientists could not explain why the emission spectra of atoms consist of lines

Department of Chemistry and Biochemistry CHM Reeves To explain these spectra, Neils Bohr proposed a model for the atom in which the eletron must occupy orbitals with radius proportional to the square of an integer n. Thus, The Bohr Atom where n is an integer > 0, and a 0 is the Bohr radius, 53 pm. a0a0 4a 0 9a 0

Department of Chemistry and Biochemistry CHM Reeves The total energy of an electron bound to a hydrogen atom is The Bohr Atom Bohr argued that when light is absorbed by the hydrogen atom, an electron jumps from a lower energy state (n 1 ) to a higher energy state (n 2 ). The energy of the absorbed photon equals the difference in energy between the higher and lower state. Consider the 121nm photon.

Department of Chemistry and Biochemistry CHM Reeves Although Bohr's theory was very successful at predicting the line spectrum of hydrogen, it failed to predict the spectra of any of the other atoms. The Wave Behavior of Matter Since electromagnetic radiation behaves like particles as well as waves, DeBorglie proposed that electrons (and all other forms of matter) might behave like waves. Thus, the integers found in the Bohr theory would arise naturally if the behavior of the electron were that of a standing wave.

Department of Chemistry and Biochemistry CHM Reeves For a standing wave on a string of length L: The Wave Behavior of Matter Thus, the quantization (n = integer) arises naturally from the fact that the ends are fixed.

Department of Chemistry and Biochemistry CHM Reeves DeBroglie pictured the electron as a standing waved confined to an orbital of radius r. The Wave Behavior of Matter

Department of Chemistry and Biochemistry CHM Reeves Using de Broglie's hypothesis, Irwin Schrodinger solved the hydrogen atom problem using classical "wave motion" equations. Quantum Mechanics & Atomic Orbitals The resulting wave functions were used to determine the probable locations of electrons as well as electron energies The solutions requires the existence of 3 quantum numbers, labeled n, l and m l. Results agreed exactly with the experimental results for hydrogen, and worked for other atoms as well. The orbitals predicted by the wave functions represent volumes within which there is a 90% probability of finding the electrons that occupying it.

Department of Chemistry and Biochemistry CHM Reeves Orbitals with the same value of n, the radial quantum number, are in the same shell. The larger the n value of an orbital, the larger its radius and the higher its energy. Each shell is divided into n subshells, each corresponding to a different value of l, and containing a different number of orbitals. Quantum Mechanics & Atomic Orbitals

Department of Chemistry and Biochemistry CHM Reeves How many orbitals are in the 6p subshell? Quantum Mechanics & Atomic Orbitals Which of the following subshell designations is/are not allowed? 4s: 2d: 6f:

Department of Chemistry and Biochemistry CHM Reeves Representations of Orbitals

Department of Chemistry and Biochemistry CHM Reeves The principle quantum number (n) defines the shell. The Wave Behavior of Matter The subshell is defined by a combination of two quantum numbers, n and l. The orbital is defined by a combination of three quantum numbers, n, l and m l.

Department of Chemistry and Biochemistry CHM Reeves Indicate the subshell in which each of the following orbitals is found: The Wave Behavior of Matter 3, 1, -1: 4, 2, 0: 3, 3, -3: 6, 0, -1:

Department of Chemistry and Biochemistry CHM Reeves Although orbitals are characterized by three quantum numbers, electrons that occupy the same orbital in different identical atoms display differences in magnetic properties. The Wave Behavior of Matter

Department of Chemistry and Biochemistry CHM Reeves Although orbitals are characterized by three quantum numbers, electrons that occupy the same orbital in different identical atoms display differences in magnetic properties. Many-electron atoms The difference in the paths of silver atoms was caused by difference in the direction of the magnetic field associated with the electron's spin.

Department of Chemistry and Biochemistry CHM Reeves Electron spin is quantized with quantum numbers m s = or Many-electron atoms Thus, the electron is characterized by four quantum numbers. The Pauli Exclusion Principle states: No two electrons in the same atom can have the same four quantum numbers. Since electrons in the same orbitals have the same values of n, l, and m l, they must have different values of m s. The Pauli Exclusion principle requires that each orbital contain no more than two electrons of opposite spin. The Aufbau principle states that electrons be placed in the atom in the order of lowest to highest energy orbitals.

Department of Chemistry and Biochemistry CHM Reeves In hydrogen and other one electron systems (He +, Li 2+ ), the energy of an orbital depends only on the value of the quantum number n. Many-electron atoms Energy

Department of Chemistry and Biochemistry CHM Reeves For all atoms or ions with two or more electrons, the energy depends on n and l. Many-electron atoms Energy

Department of Chemistry and Biochemistry CHM Reeves The electronic configuration of an element lists the occupied subshells followed by a superscript indicating the number of electrons it contains. H: He: Li: Be: B: C: N: O: F: Ne: 15 P: 24 Cr: Electronic Configurations

Department of Chemistry and Biochemistry CHM Reeves For an anion, add the extra electrons to the lowest energy orbital that is not fully occupied (LUMO). Electronic Configurations 17 Cl: 17 Cl - : 33 As: 33 As 3 - : For a cation, remove the extra electrons from the highest energy orbital that is occupied (HOMO), except that valence s electrons are removed before the d electrons in the shell below. 20 Ca: 20 Ca 2+ : 26 Fe: 26 Fe 2+ : 26 Fe 3+ :

Department of Chemistry and Biochemistry CHM Reeves Orbital Diagrams depict electrons as arrows whose directions indicate their spin. Many-electron atoms Energy 7 N:1s 2 2s 2 2p 3 OR Hund's rule: When electrons fill degenerate orbitals, the lowest energy (ground state) configuration occurs when the maximum number of electrons have parallel spins.

Department of Chemistry and Biochemistry CHM Reeves Periodic Connections