CHE CHEMICAL CONCEPTS AND STRUCTURE ELECTRONS IN ATOMS LECTURES Dr David J McGarvey

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1 CHE CHEMICAL CONCEPTS AND STRUCTURE ELECTRONS IN ATOMS LECTURES Dr David J McGarvey

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3 TOWARDS A MORE SOPHISTICATED VIEW OF CHEMICAL BONDING Recall that we asked which of the following is the correct shape for allene? trigonal planar linear epg epg & mg & mg H H? C C C H 2 C C CH 2? H H ALLENE H H C C C H H To answer this question (and others) we need to develop our understanding of chemical bonding to a higher level of sophistication; this requires us to start with a detailed examination of the properties of electrons in atoms.

4 ELECTRONS IN ATOMS An understanding of the electronic structure of atoms is fundamental to a deeper understanding of the chemical and spectroscopic behaviour of the elements and the compounds they form. The purpose of this section is to understand how electrons are arranged within neutral and ionised atoms. We can then use this knowledge base to explore more sophisticated models of chemical bonding in the next section. Chapters 2, (11, 16) Chapter 1 Chapter 4

5 LEARNING OUTCOMES Apply the Rydberg equation to predict the positions of spectral lines for hydrogenic atoms. Define and classify atomic orbitals in terms of the quantum numbers (n, l, m l ) and the nomenclature s, p, d, f etc Relate properties of atomic orbitals (e.g. energy, shape, directional) to the quantum numbers n, l, m l Determine permitted values for l and m l for a given value of n Sketch the shapes (boundary surfaces) of s, 2p and 3d-orbitals with reference to x, y, z axes.

6 ELECTRONS IN ATOMS Here is a familiar cartoon of electrons in an atom : But it isn t like this! The reality is much more complex! The behaviour of electrons in atoms can be derived and described using quantum mechanics (QM). At this stage we are not going to be concerned with the mathematical aspects of QM, but we will study in detail the results and concepts yielded by the applications of QM to electrons in atoms.

7 TWO IMPORTANT FEATURES OF THE QUANTUM WORLD In classical systems (described by Newton s laws) the position of an object can be specified exactly. In quantum systems, we can only talk about the probability of a particle being at a particular location: some regions have higher probability, and some lower. Chemical Structure and Reactivity: an Integrated Approach, James Keeler and Peter Wothers, OUP 2008

8 TWO IMPORTANT FEATURES OF THE QUANTUM WORLD In classical systems which is what we experience directly in our day-to-day lives energy can vary smoothly from one value to another. In quantum systems, which applies to very small particles, the energy can only have certain values, called energy levels. We can see direct evidence of this if we look at the light emitted from a hydrogen or neon discharge lamp. Chemical Structure and Reactivity: an Integrated Approach, James Keeler and Peter Wothers, OUP 2008

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10 THE HYDROGEN ATOM SPECTRUM

11 The hydrogen atom consists of a proton and an electron. The energy of the electron is restricted to certain values; i.e. its energy is quantised. For current purposes we can visualise the electron as being able to occupy orbits specified by a quantum number n, which is restricted to integral values: n = 1, 2, 3, 4,... THE HYDROGEN ATOM It is also customary to refer to shells (e.g. the n = 1 shell). The higher the value of n, the higher the energy.

12 THE ORIGIN OF EMISSION LINES IN THE HYDROGEN ATOM SPECTRUM n = 3 2 n = 4 2 n = 5 2

13 THE HYDROGEN ATOM SPECTRUM Atomic spectroscopy forms the basis of some exceptionally sensitive and selective analytical techniques (Atomic Absorption Spectroscopy (AAS), Inductively Coupled Plasma Atomic Emission Spectroscopy (ICP-AES)) Shriver & Atkins 2009

14 ATOMIC SPECTRA, ENERGY LEVELS & LIGHT c E h h c 1 hc Atkins and Jones 2005 When an electron in an atom undergoes a transition from a higher energy level to a lower one, it loses energy by emitting a photon. Chemical Structure and Reactivity: an Integrated Approach, James Keeler and Peter Wothers, OUP 2008

15 Self-Test: Calculate the energy (in kj mol -1 ) associated with blue light of wavelength 400 nm. Avogadro constant N A = x mol -1 Planck constant h = x J s Velocity of light (vacuum) c = x 10 8 m s -1 nanometre nm = 10-9 m

16 THE HYDROGEN ATOM SPECTRUM AND THE RYDBERG EQUATION 1890: Rydberg noticed that all lines in the hydrogen atom emission spectrum fit a general empirical equation. 1 1 RH 2 2 nl nu L lower U upper R H 4 R H 9 n L =3 n L =2 n L =1 Atkins & Jones 2009 R H n L =4 Chemical Structure and Reactivity: an Integrated Approach, James Keeler and Peter Wothers, OUP 2008

17 Self-Test: Calculate (in nm) for the transition from n U = 3 n L = 2. Rydberg constant R H = x 10 5 cm -1 upper U lower L n n R U L H

18 THEORY AND EXPERIMENT The pattern of lines in the H-atom spectrum is an experimental observation. The Rydberg formula is empirical. But is there a theory that could be used to predict the behaviour of the electron in the H-atom and hence predict its spectrum? The answer, of course, is yes; Quantum Mechanics and the Schrödinger equation. The possible energies of an electron in an H-atom (energy levels) and its associated spatial properties can be determined by solving an equation called the Schrödinger equation.

19 THE SCHRÖDINGER EQUATION FOR THE HYDROGEN ATOM CAN BE SOLVED EXACTLY The key feature of the Schrödinger equation is its solution, the wavefunction (). For the electron in a hydrogen atom, the wavefunctions are known as atomic orbitals. The atomic orbitals can only be viable (acceptable) if the energy is quantised. The result is the following expression for the energy of the electron in the hydrogen atom: E n RH n 1, 2 n 3,... We say that the energy is quantised and each energy level has an associated quantum number, n, which affects its energy. The value of the Rydberg constant R H arises naturally from the theory! 2,

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21 THE SCHRÖDINGER EQUATION FOR THE HYDROGEN ATOM CAN BE SOLVED EXACTLY More generally, for hydrogenic atoms (an atom with 1 electron) of atomic number Z, the energy of the electron in the atom is given by: RH Z En 2 n n 1, 2, 3,... 2 R H 9 R H 4 R H An example of a hydrogenic atom is He + (Z=2) R H 4R H

22 THE SCHRÖDINGER EQUATION FOR THE HYDROGEN ATOM CAN BE SOLVED EXACTLY Overall, the atomic orbitals require the specification of three quantum numbers: n, l, m l. n = principal quantum number - energy. l = angular momentum quantum number - shape. l=0 l=1 l=2 m l = magnetic quantum number direction. m l =0 m l =+1 m l =-1 Chemical Structure and Reactivity: an Integrated Approach, James Keeler and Peter Wothers, OUP 2008

23 HYDROGENIC ATOMIC ORBITALS The possible values of the quantum numbers are interconnected such that the value of n determines the possible values of l and hence m l. n 1,2,3,... l 0,1,2,...( n 1) l=0 s-orbital l=1 p-orbital l=2 d-orbital m l l, l 1, l 2... l l=3 f-orbital l=4 g-orbital For hydrogenic atoms (i.e., one electron atoms), orbitals with the same value of n are degenerate; i.e. of equal energy.

24 n 1,2,3,... l=0 s-orbital l=1 p-orbital l 0,1,2,...( n 1) l=2 d-orbital m l l, l 1, l 2... l l=3 f-orbital l=4 g-orbital

25 HYDROGENIC ATOMIC ORBITALS The number of possible orbitals for a specified value of n is equal to n 2 The value of n gives the number of types of orbital (subshells). For example, for n=3, there are 9 orbitals and 3 types of orbital (i.e. three subshells): Types of orbital: 3s, 3p & 3d For hydrogenic atoms, the energy only depends on one quantum number: n i.e. for a hydrogenic atom, the energy of 2s = 2p and the energy of 3s = 3p = 3d.

26 Self-Test: How many orbitals are there with n=4? What orbitals correspond to (i) n=5, l=2, (ii) n=4, l=3? What are n, l and the possible values of m l for 5p orbitals?

27 HYDROGENIC ATOMIC ORBITALS Atkins & Jones 2009

28 Self-Test: Complete the following table n l m l values Orbital name

29 BOUNDARY SURFACE REPRESENTATIONS: 2s & 2p-ORBITALS A boundary surface representation of an orbital is a surface within which there is typically a 95% probability of finding the electron. Different shades reflect different sign of. Red is +ve and blue is ve. The sign of has nothing to do with charge. Chemical Structure and Reactivity: an Integrated Approach, James Keeler and Peter Wothers, OUP 2008

30 BOUNDARY SURFACE REPRESENTATIONS: 3p-ORBITALS Notice that the general shape is similar to the 2p orbitals see later! Chemical Structure and Reactivity: an Integrated Approach, James Keeler and Peter Wothers, OUP 2008

31 BOUNDARY SURFACE REPRESENTATIONS: 3d-ORBITALS Chemical Structure and Reactivity: an Integrated Approach, James Keeler and Peter Wothers, OUP 2008

32 BOUNDARY SURFACE REPRESENTATIONS: 4f-ORBITALS Chemical Structure and Reactivity: an Integrated Approach, James Keeler and Peter Wothers, OUP 2008

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