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The Current Model of the Atom Name This Element Building on Bohr Quantum Mechanics • Uses mathematical equations to describe the wave properties of subatomic particles • It’s impossible to know the exact position, speed and direction of an electron (Heisenberg Uncertainty Principle) • So Bohr’s “orbits” were replaced by orbitals • The simple Bohr model was unable to explain properties of complex atoms • Only worked for hydrogen • A more complex model was needed… Orbits – A wave function that predicts an electron’s energy and location within an atom – A probability cloud in which an electron is most likely to be found Orbitals - Bohr - Quantum Mechanics - 2-dimensional ring - 3-dimensional space - Electron is a fixed - Electrons are a variable distance from nucleus distance from nucleus - 2, 8, or 18 electrons per - 2 electrons per orbital orbit Wave Particle Duality • Experimentally, DeBroglie found that light had both wave and particle properties • Therefore DeBroglie assumed that any particle (including electrons) traveled in waves • Wavelengths must be quantized or they would cancel out 1 Heisenberg’s Uncertainty Principle • Due to the wave and particle nature of matter, it is impossible to precisely predict the position and momentum of an electron • SchrÖdinger’s equation can be used to determine a region of probability for finding an electron (orbital) • Substitute in a series of quantum numbers to solve the wave function Schroedinger’s Cat • What’s up with the cat? Quantum Numbers • Four numbers used to describe a specific electron in an atom • Every electron in an atom has its own specific set of quantum numbers • Recall: Describes orbitals (probability clouds) Schroedinger's Equation A description of each variable: h - Planck's Constant - Usually (h/2π) is called hbar, and has a value of 0.6582*10-15 eV·s m -mass of the particle being examined. Ψ - The wave function. This is what is usually being computed using Schroedinger's Equation. V - This is the potential energy of the described particle. j - The imaginary number, being equal to √-1. x - Position t - Time Defining the orbital • Schroedinger’s calculations suggest the maximum probability of finding an e- in a given region of space with a particular quantity of energy (orbital) • Different orbitals are present in atoms having different sizes, shapes and properties • There are 4 parameters (called quantum numbers) that define the characteristics of these orbitals and the electrons within them • This information provides the basis for our understanding of bonding Quantum Numbers • Since an orbital is a 3-D space, we need at least 3 variables to define it, though there are 4 quantum numbers • Each electron has a unique set of numbers just as each point on a twodimensional graph has a unique set of two numbers (x, y). 2 The Pauli Exclusion Principle • All four quantum numbers are needed for a complete description of each electron in an atom. • The allowed values of the four quantum numbersCan areonly restricted be certainand numbers interdependent, indicating next number depends on the first the influence of quantization. • no two electrons in an atom can have the same set of four quantum numbers, • a complete set of four quantum numbers is a unique description of a single electron in a multielectron atom. • “the address of the electron” 1. Principal Quantum Number (n) Distance between energy levels decreases as n increases • the integer that Bohr used to label the orbits and energy levels of an atom • Tells us the size of the orbital • n= 1, 2, 3…..∞, n € R • The larger n is, the greater the average distance from the nucleus (less stable) • The energy gap between successive levels gets smaller as n gets larger • The greatest number of electrons possible in each energy level is 2n2 2. Angular momentum quantum number (l) • Is a sublevel of n that tells the shape of the orbital • The values of l depend on n • For any given n, l = 0 to n-1 • The values of l are designated by the letters s, p, d, f, g, h • The number of sublevels is equal to the value of n – If n=1, l = 0 s – If n=2, l = 0, 1 s, p – If n=3, l = 0, 1, 2 s, p, d Shape of orbitals l Name of orbital Shape 0 1 2 3 s p d f Sphere (1 lobe) 2 lobes 4 lobes 8 lobes 3 Shapes of s, p, and d-Orbitals d-orbitals Shapes of orbitals video Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 336 Shape of f orbitals 3. Magnetic quantum number (ml) • This number indicates the orientation of the orbital in 3-D space • m has values related to l, ml = -l, 0, +l – If n = 1, l = 0, ml = 0 – If n = 2, l = 0, 1, ml = -1, 0, +1 (this indicates that there are 3 orbits that have the same energy and shape, but differ only in their orientation in space) – Maximum number of orientations is n2 Principal Energy Levels 1 and 2 The First Three Quantum Numbers Quantum numbers video 4 4. Spin quantum number (ms) Quantum Numbers Summary Chart Name • The rotation of the electron in the orbital is either clockwise or counterclockwise • ms can have values of + ½ or – ½ • Qualitatively we refer to the spin as either clockwise or counterclockwise or up or down Symbol Allowed Values Property Principal n positive integers 1,2,3… Orbital size and energy level Secondary l Integers from 0 to (n-1) Orbital shape (sublevels/subshells) Magnetic ml Integers –l to +l Orbital orientation Spin ms +½ or –½ Electron spin Direction Four numbers are required to describe the energy of an electron in an atom 5