Summary ATOMS AND ATOMIC STRUCTURE

Basic Postulates of Quantum Theory 1. Atoms and molecules can exist only in certain energy states. In each energy state, the atom or molecule has a definite energy. When an atom or molecule changes its energy state, it must emit or absorb just enough energy to bring it to the new energy state (the quantum condition). 2. Atoms or molecules emit or absorb radiation (light) as they change their energies. The frequency of the light emitted or absorbed is related to the energy change by a simple equation. 2 mc hc hE   The allowed energy states of atoms and molecules can be described by sets of numbers called quantum numbers. • Quantum numbers are the solutions of the Schrodinger, Heisenberg & Dirac equations. • Four quantum numbers are necessary to describe energy states of electrons in atoms – n, , m , ms          2 2 2 m r t V r t r t i r t t  ( , ) ( , ) ( , ) ( , )  Schroedinger 3-dimensional time independent equation Heisenberg’s uncertainty Equation Dirac’s quantum mechanical model 1. The Principal quantum number has the symbol – n. n = 1, 2, 3, 4, ...... “shells” n = K, L, M, N, ...... The electron’s energy depends principally on n and tells the average relative distance of the electron from the nucleus. – As n increases for a given atom, so does the average distance of the electrons from the nucleus. – Electrons with higher values of n are easier to remove from an atom. n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 l= 0 l = s l= 1 l = p l = 2 l = d l = 3 l = f n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 2. The azimuthal quantum number has the symbol . Ø describes the shape of the region of space occupied by the electron Ø When linked with n defines the energy of the electron, All wave functions that have the same value of both n and l form a subshell = 0, 1, 2, 3, 4, 5, .......(n-1) = s, p, d, f, g, h, .......(n-1) 3. The symbol for the magnetic quantum number is m . m = - , (- + 1), (- +2), .....0, ......., ( -2), ( -1), • If = 0 (or an s orbital), then m = 0. – There is only 1 value of m . Thus there is one s orbital per n value. n  1 • If = 1 (or a p orbital), then m = -1,0,+1. – There are 3 values of m . Thus there are three p orbitals per n value. n  2 • If = 2 (or a d orbital), then m = -2,-1,0,+1,+2. – There are 5 values of m . Thus there are five d orbitals per n value. n  3 • If = 3 (or an f orbital), then m = -3,-2,-1,0,+1,+2, +3. – There are 7 values of m . Thus there are seven f orbitals per n value, n – Theoretically, this series continues on to g,h,i, etc. orbitals. • Practically speaking atoms that have been discovered or made up to this point in time only have electrons in s, p, d, or f orbitals in their ground state configurations. • Each wave function with an allowed combination of n, l, and ml values describes an atomic orbital, a particular spatial distribution for an electron © 2006 Brooks/Cole - Thomson • Atomic orbitals are regions of space where the probability of finding an electron about an atom is highest. • s orbital properties: • There is one s orbital per n level. • = 0 • 1 value of m l= 0 l = s n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7