Chapter 6: Electronic Structure of Atoms

Transcription

1 Chapter 6: Electronic Structure of Atoms Recommended Text Problems 5, 8, 15, 17, 19, 21, 25, 29ab, 31, 49, 51, 53, 55ab, 57ac, 59, 63, 65, 67abcd, 71, 73, 90 1

2 The Nature of Light Case 1 Stand outside in the sun. The shadow your body makes in sunlight suggests that light travels in straight lines from the sun and is blocked by your body. In this, light behaves like The Nature of Light Case 2 Place two sheets of glass together with a little water between them. With care, you will see fringes. These are formed by 2

3 The Nature of Light Light is a electromagnetic radiation It contains 2 components Electric and magnetic components Waves The wavelength (λ) The frequency (ν) For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency. 3

4 Electromagnetic Radiation All electromagnetic radiation travels at the same velocity: the speed of light (c), m/s. Therefore, Example: What is the wavelength of yellow light with a frequency of 5.09 x s -1? (Note: s -1, commonly referred to as Hertz (Hz) is defined as cycles or waves per second.) 4

5 More Example: What is the frequency of violet light with a wavelength of 408 nm? Photoelectric Effect In 1905, Albert Einstein proposed that light had both wave and particle properties as observed in the photoelectric effect. He concluded that energy is proportional to frequency: 5

6 Photoelectric Effect The photoelectric effect is the ejection of electrons from the surface of a metal when light shines on it. Electrons are ejected only if the light exceeds a certain threshold frequency. Violet light, for example, will cause potassium to eject electrons, but no amount of red light (which has a lower frequency) has any effect. Example What is the energy of a photon corresponding to radio waves of frequency x 10 6 s -1? 6

7 Line Spectrum For atoms and molecules one does not observe a continuous spectrum, as one gets from a white light source. Only a line spectrum of discrete wavelengths is observed. Line Spectrum Niels Bohr adopted Planck s assumption and explained: 7

8 Line Spectrum The Energy of an allowed orbital in a hydrogen atom is Line Spectrum The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation: Lyman series: Balmer : Paschen 8

9 Example: Predict which of the following electronic transitions produces the spectral line having the longest wavelength: n = 2 to n = 1, n = 3 to n = 2, or n = 4 to n = 3. Example: Calculate the energy of a photon of light emitted from a hydrogen atom when an electron falls from level n = 3 to level n = 1. 9

10 The Wave Nature of Matter Louis de Broglie proposed that if light can have material properties, matter should exhibit wave properties. He demonstrated that the relationship between mass and wavelength was Example The de Broglie relation shows that a baseball (0.145 kg) moving at about 60 mph (27 m/s) has a wavelength of about 1.7 x m. 10

11 Practice What is the wavelength of an electron moving with a speed of m/s? The mass of the electron is kg. The Uncertainty Principle Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known: 11

12 Quantum Mechanics Although we cannot precisely define an electron s orbit, we can obtain the probability of finding an electron at a given point around the nucleus. Erwin Schrodinger defined this probability in a mathematical expression called a wave function, denoted ψ (psi). ψ 2 Quantum Mechanics 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. An orbital is described by a set of three quantum numbers. 12

13 Principal Quantum Number (n) The principal quantum number, n, describes the on which the orbital resides. Angular Momentum Quantum Number (l) This quantum number defines the of the orbital. 13

14 Magnetic Quantum Number (m l ) The magnetic quantum number describes the of the orbital. Magnetic Quantum Number (m l ) Orbitals with the same value of n form a shell. Different orbital types within a shell are subshells. 14

15 Example: a. Predict the number of subshells in the fourth shell, that is, for n = 4. b. Give the label for each of these subshells. c. How many orbitals are in each of these subshells? s Orbitals The value of l for s orbitals is 0. They are spherical in shape. The radius of the sphere increases with the value of n. 15

16 s Orbitals Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n 1 nodes, or regions where there is 0 probability of finding an electron. p Orbitals The value of l for p orbitals is 1. They have two lobes with a node between them. 16

17 d Orbitals The value of l for a d orbital is 2. Four of the five d orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center. Energies of Orbitals For a one-electron hydrogen atom, Degenerate. 17

18 Spin Quantum Number, m s 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. Spin Quantum Number, m s This led to a fourth quantum number, the spin quantum number, m s. The spin quantum number has only 2 allowed values: +1/2 and 1/2. 18

19 Pauli Exclusion Principle No two electrons in the same atom can have exactly the same energy. Therefore, no two electrons in the same atom can have identical sets of quantum numbers. Electron Configurations This shows the distribution of all electrons in an atom. Each component consists of 4p 5 19

20 Orbital Diagrams Each box in the diagram represents Half-arrows represent The direction of the arrow represents the Hund s Rule 20

21 Energy Orbital Energy Levels in Multielectron Systems 4s 3p 3s 2p 2s 1s 3d Electron Configuration Here are a few examples. Using the abbreviation [He] for 1s 2, the configurations are Z=4 Z=3 Beryllium Lithium 21

22 Electron Configuration With boron (Z=5), the electrons begin filling the 2p subshell. Z=5 Boron Z=6 Carbon Z=7 Nitrogen Z=8 Oxygen Z=9 Fluorine Z=10 Neon 1 s 2 2 s 2 2 p 2 Electron Configuration Note that elements within a given family have similar configurations. The Group IIA elements are sometimes called the alkaline earth metals. Beryllium Magnesium Calcium 22

23 Electron Configuration Note that elements within a given family have similar configurations. Helium Neon Argon Krypton Example Draw the orbital diagram for the electron configuration of oxygen, atomic number 8. How many unpaired electrons does an oxygen atom possess? 23

24 More Example What is the characteristic valence electron configuration of the group 7A elements, the halogens? Practice Makes Perfect (a) Write the electron configuration for bismuth, element number 83. (b) Write the condensed electron configuration for this element. (c) How many unpaired electrons does each atom of bismuth possess? 24

25 Some Anomalies Some irregularities occur when there are enough electrons to This occurs because Example Boron, atomic number 5, occurs naturally as two isotopes, 10 B and 11 B, with natural abundances of 19.9% and 80.1%, respectively. a. In what ways do the two isotopes differ from each other? Does the electronic configuration of 10 B differ from that of 11 B? b. Draw the orbital diagram for an atom of 11 B. Which electrons are the valence electrons? c. Indicate three major ways in which the 1s electrons in boron differ from its 2s electrons. d. Elemental boron reacts with fluorine to form BF3, a gas. Write a balanced chemical equation for the reaction of solid boron with fluorine gas. e. H o f for BF 3 (g) is kj mol 1. Calculate the standard enthalpy change in the reaction of boron with fluorine. f. When BCl3, also a gas at room temperature, comes into contact with water, the two react to form hydrochloric acid and boric acid, H 3 BO 3, a very weak acid in water. Write a balanced net ionic equation for this reaction. 25

26 Definitions/Principals wavelength (λ) frequency (ν) the photoelectric effect. The uncertainty principle principal quantum number, n angular momentum quantum number, l magnetic quantum number, m l spin quantum number, m s degenerate. spin quantum number, m s Hund s rule Pauli exclusion principle 26