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Chapter 11 Notes Modern Atomic Theory Introduction You may recall that one of the ideas of Dalton’s Atomic Theory was that all elements are composed of indivisible particles called atoms. For about 50 years past the time of John Dalton (1766-1844) this idea remained. However, around 1900 J. J. Thomson discovered the presence of electrons - small, light quantities of negative charge. This chapter focuses on the electron and the arrangement of electrons in atoms. Models of the Atom Our description of the atom has evolved over the years. Below is a brief description of the four basic models that have existed through the years. 1) Thomson Model This model is sometimes called the plum pudding model. The negative electrons (the plums) are embedded a positive matrix (the pudding). This early model does not acknowledge the existence of the nucleus. 2) The Rutherford Model This model is a direct result of the discovery of the nucleus by Rutherford in 1911. In this model, stationary electrons surround a center of positive charge. 3) The Bohr Model In 1913 Niels Bohr proposed a model in which the electrons circled the nucleus, like the planets orbit the sun. This model is sometimes called the planetary model. This model also proposed a very insightful idea: that the electrons could only occupy certain positions around the nucleus, and the farther out electrons got, the greater the electron’s energy. An electron could only move to a higher energy level if it acquired a certain amount (a quantum) of energy. 4) The Quantum Mechanical Model In 1926, Erwin Schrodinger wrote a mathematical equation to describe the location and speed of an electron in an atom. This model is based on probability. This model describes the location in terms of the region in which one will find an electron 90% of the time. The Wave-like Nature of the Electron Every object has a wave-like nature to it. For most common objects, however, the macroscopic quantities are enormous compared to the wave behavior; hence, we do not normally associate wave characteristics with common objects. The electron, however, is sufficiently small (it has very little mass) and so the wave characteristics are much more pronounced. Here, we will examine the basics of waves. Basics of Waves The picture below shows a typical representation of a wave. The wavelength () is the distance between adjacent points on a wave. It is usually measured in meters. The frequency () of a wave is how many crests pasts by a certain point per second. Frequency is usually measured in Hertz (Hz). One Hz is a wave per second, 1/sec, or sec-1. There is an inverse relationship between frequency and wavelength - when one goes up the other goes down, and vice versa. Speed of a Wave The speed of a wave is given by the product of the frequency and wavelength. If the wave is an electromagnetic wave, such as light, then the speed of the wave through a vacuum is a constant of 3.00 X 108 m/s. c = EXAMPLE: What is the frequency of light that has a wavelength of 580. nm? (1 nm = 1 nanometer = 1 X 10-9 m) EXAMPLE: What is the wavelength of radiation that has a frequency of 6.00 X 1017 Hz? Energy of a Photon Einstein though of light as little packets of energy known as “photons”. The energy of a photon is given by the product of Planck’s constant times the frequency. E=h where h = Planck’s constant = 6.63 X 10-34 Jsec EXAMPLE: How much energy is in a photon of frequency 6.00 X 1017 Hz? EXAMPLE: Consider an atom with the energy levels described in the picture below. Suppose an electron falls from an excited state (fourth energy level) back to the ground state (first energy level). What will be the wavelength of light given off? Arrangement of Electrons in Atoms There are four levels of organization to describe the location of an electron in any particular atom. 1) Principal Energy Level - Describes in very general terms how far away from the nucleus an electron can be found. It is given the symbol n. 2) Sublevel - There are four different sublevels called s, p, d, and f. The first principal energy level has only one sublevel, called the “1s”. The second principal energy level has two sublevels: a “2s” and a “2p”. The third principal energy level has three sublevels: a “3s”, a “3p” and a “3d”. The fourth and all subsequent principal energy levels have four sublevels. For n = 4, there is the 4s, 4p, 4d and 4f. Theoretically, there exists a “5g” in the fifth principal energy level, but we run out of electrons before we begin filling it. 3) Orbitals - The s sublevel contains only one orbital, which is spherically shaped. The p sublevel contains three orbitals, which are shaped like dumbells and are oriented mutually perpendicular to each other (like the x, y and z axes). There are five d orbitals, and seven f orbitals. Pictures of some orbitals can be found on pages 372-374 in the text. 4) Spin - Each orbital can contain two electrons, one with spin up and the other with spin down. Two electrons with the same spin will never occupy the same orbital. (Furthermore, the first electron in an orbital is spin up, according to the Law of Maximum Multiplicity.) The table below summarizes our results so far: Principal Energy Level Number of Sublevels Types of Sublevels Maximum number of Electrons n=1 1 1s 2 n=2 2 2s, 2p 8 n=3 3 3s, 3p, 3d 18 n=4 4 4s, 4p, 4d, 4f 32 Rules for Placing Electrons 1) Aufbau Principle - Electrons enter orbitals of lowest energy first. 2) Pauli Exclusion Principle - An orbital can only contain two electrons, and these electrons must have opposite spin. (Another way of stating this principle is to say that no two electrons in an atom can have the same four quantum numbers.) 3) Hund’s Rule - Within a sublevel, electrons enter singly before pairing up. We will use these rules to place electrons in atoms in some examples that will follow. Energy Level Diagram for Sublevels Below is a diagram which arranges sublevels in order of increasing energy. Each box represents an orbital. You don’t have to memorize this table. There is an easier way. That way involves making diagram shown on the bottom right corner. EXAMPLES: Fill in the orbital diagram, and give the electron configuration of the following elements: H 1s He 1s 2s Li 1s 2s Be 1s 2s B 1s 2s C 2p 1s 2s N 2p 1s 2p 2s O 1s 2s F Ar Ca V 2p 1s 2s Ne 2p 2p 1s 3s 3p 2s 2p 3d 1s 4s 4p 4d 3s 3p 3d 2s 2p 4f 1s 4s 4p 4d 3s 3p 3d 2s 2p 1s 4f Finding the Last Electron in an Atom (The Easy Way)! EXAMPLE: What is the last electron in the following elements: (a) V EXAMPLE: (b) Ba (c) Pb Write the electron configuration (long-hand and shortcut) for the following elements: Nickel (Z = 28) Bromine (Z = 35) Lead (Z = 82) Paramagnetism and Diamagnetism in Elements If an element has unpaired electrons in its electron configuration, that element will be paramagnetic and will be bent by a magnetic field. An element that has no unpaired electrons is diamagnetic, and will not be bent in a magnetic field. Example: Write the electron configuration, and determine if the following elements are paramagnetic or diamagnetic. Mg S Exceptional Electron Configurations Some of the elements have electron configurations that deviate from the norm. The driving force for this deviation is the extra stability offered by filled and half-filled sublevels. The most well-known exceptions are chromium and copper. The 3d sublevel steals an electron from the 4s for added stability. Draw the configurations for copper and chromium below: EXPECTED CONFIGURATIONS Cr Cu ACTUAL CONFIGURATIONS Cr Cu Configurations of Ions Atoms gain or lose electrons to form ions. To write the configuration of an anion, just add an appropriate number of electrons to the configuration. When forming a cation, remove electrons in the configuration. For transition metals (the d-block), electrons will be lost from the ns sublevel before losing electrons from the (n-1)d sublevel. The following examples will demonstrate these procedures. EXAMPLES: Write the electron configurations of the following ions: O-2 Al+3 Co+3 Quantum Numbers Each electron in every atom is assigned a set of four quantum numbers. According to the Pauli exclusion principle, no two electrons can have the exact quantum numbers. The rules are stated below. 1) Principal Quantum Number (n) - Just the value of the principal energy level. 2) Angular Momentum Quantum Number (l) - This number is determined from the type of sublevel. The numbers are 0, 1, 2, and 3 for s, p, d, and f sublevels, respectively. 3) The Magnetic Quantum Number (ml) - This number runs from -l to +l and states which orbital the electron is in. 4) The Spin Quantum Number (ms) - This is +1/2 for the first electron in an orbital, and -1/2 for the second electron in an orbital. EXAMPLES: Write the quantum numbers for each electron 1s1 4d6 1s2 2p1 4d3 2p4 EXAMPLES: Determine the electron for the following sets of quantum numbers. 3, 2, 0, -1/2 EXAMPLE: 2, 1, 1, +1/2 3, 3, 0, +1/2 If the first quantum number is a three, what are the limits on the second and third quantum numbers?