Chapter 6 Quantum Mechanical Model & Electron Configurations Chemistry, The Central Science, 10th edition Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten Chapter 6 Quantum Mechanical Model & Electron Configurations . 1

Waves To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation. The distance between corresponding points on adjacent waves is the wavelength (). 2

Waves 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. 3

Electromagnetic Radiation All electromagnetic radiation travels at the same velocity: the speed of light (c), 3.00  108 m/s. Therefore, c =  4

The Nature of Energy 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. 5

The Nature of Energy Einstein used this assumption to explain the photoelectric effect. He concluded that energy is proportional to frequency: E = h where h is Planck’s constant, 6.63  10−34 J-s. 6

The Nature of Energy Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light: c =  E = h 7

The Nature of Energy Another mystery involved the emission spectra observed from energy emitted by atoms and molecules. 8

The Nature of Energy One does not observe a continuous spectrum, as one gets from a white light source. Only a line spectrum of discrete wavelengths is observed. 9

The Nature of Energy Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: Electrons in an atom can only occupy certain orbits (corresponding to certain energies). 10

The Nature of Energy Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom. 11

The Nature of Energy Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by E = h 12

The Wave Nature of Matter Louis de Broglie posited that if light can have material properties, matter should exhibit wave properties. 13

The Uncertainty Principle Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known: In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself! (x) (mv)  h 4 14

Quantum Mechanics Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. It is known as quantum mechanics. 15

Quantum Mechanics The wave equation is designated with a lower case Greek psi (). The square of the wave equation, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time. 16

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 for 2 electrons. An orbital is described by a set of three quantum numbers. 17

Quantum Mechanical Model & Orbitals describes the energy level on which the orbital resides. defines the shape of the orbital. Determines the orientation in space of the orbitals of any given type in a sublevel Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc. 18

Magnetic Quantum Number, ml Orbitals with the same value of n (energy level) form a shell. Different orbital types within a shell are subshells. (3s, 3p, 3d) 19

Quantum Mechanical Explanation of Atomic Spectra Each wavelength in the spectrum of an atom corresponds to an electron transition between orbitals. When an electron is excited, it transitions from an orbital in a lower energy level to an orbital in a higher energy level. When an electron relaxes, it transitions from an orbital in a higher energy level to an orbital in a lower energy level. Electrons in high energy states are unstable, a photon of light is released whose energy equals the energy difference between the orbitals. Each line in the emission spectrum corresponds to the difference in energy between two energy states.

Quantum Leaps

Electron Probabilities and the Shapes of Orbitals 1s Orbital (n = 1, l = 0, mι= 0) S = spherical shape cross-section: 剖面

The Three p Orbitals (l = 1, mι= –1, 0, +1) Three values of mι gives three p orbitals in the p subshell mι= –1 mι= 0 P = dumbbell shaped like two balloons tied at the knots

The Five d Orbitals (l = 2, mι= –2, –1, 0, +1, +2) Five values of mι gives five d orbitals in the d subshell d orbitals shape: are mainly like four balloons tied at the knots.

The Seven f Orbitals f orbitals shape: are mainly like eight balloons tied at the knots.

Energy of orbitals S < p < d< f S orbitals for an energy level are filled first with electrons since they have the lowest amount of energy F orbitals for an energy level are filled last since they have the greatest energy. Lower energy levels are filled before higher energy levels 1s before 2s

Spin 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. 27

Pauli Exclusion Principle No two electrons in the same atom can have exactly the same energy. For example, no two electrons in the same atom can have identical sets of quantum numbers. 28

Electron Configurations Distribution of all electrons in an atom. Consist of Number denoting the energy level. Letter denoting the type of orbital. Superscript denoting the number of electrons in those orbitals. 29

Orbital Diagrams Each box represents one orbital. Half-arrows represent the electrons. The direction of the arrow represents the spin of the electron. 30

Orbital Diagrams Each box represents one orbital. Half-arrows represent the electrons. The direction of the arrow represents the spin of the electron. 31

Periodic Table We fill orbitals in increasing order of energy. Different blocks on the periodic table, then correspond to different types of orbitals. 32

Electron Configuration Practice Potassium (K) Long hand electron configuration 1s22s22p63s23p64s1 Kernel Structure (noble gas configuration) [Ar]4s1 Orbital Diagram