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CHE-10047
CHEMICAL CONCEPTS AND STRUCTURE
ELECTRONS IN ATOMS LECTURES 1-2
2011-2012
Dr David J McGarvey
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
?
H2C C CH2
ALLENE
C C C
?
H
H
H
H
H
C C C
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.
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
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 , ml) and the nomenclature s, p, d, f etc
 Relate properties of atomic orbitals (e.g. energy, shape,
directional) to the quantum numbers n, l , ml
 Determine permitted values for l and ml for a given value of n
 Sketch the shapes (boundary surfaces) of s, 2p and 3d-orbitals
with reference to x, y, z axes.
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.
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
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
THE HYDROGEN ATOM SPECTRUM
http://jersey.uoregon.edu/vlab/elements/Elements.html
THE HYDROGEN ATOM
 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, .....∞
 It is also customary to refer to
shells (e.g. the n = 1 shell).
 The higher the value of n, the
higher the energy.
http://www.nobeliefs.com/atom.htm
THE ORIGIN OF EMISSION LINES IN
THE HYDROGEN ATOM SPECTRUM
n = 3→2
n = 4→2
n = 5→2
http://www.nobeliefs.com/atom.htm
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
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
Self-Test: Calculate the energy (in kJ mol-1) associated with
blue light of wavelength 400 nm.
Avogadro constant
NA = 6.022 x 1023 mol-1
Planck constant
h = 6.626 x 10-34 J s
Velocity of light (vacuum)
c = 2.998 x 108 m s-1
nanometre
nm = 10-9 m
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
nL=2
nL=3
nL=4


RH
9
RH
4
nL=1
© Atkins & Jones 2009
 RH
© ‘Chemical Structure and Reactivity: an Integrated
Approach’, James Keeler and Peter Wothers, OUP 2008
Self-Test: Calculate  (in nm) for the transition from nU = 3 →nL = 2.
Rydberg constant
RH = 1.09737 x 105 cm-1
 1
1 
  RH  2  2 
 nL nU 
L  lower U  upper
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.
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:
RH
En   2
n
n  1, 2, 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 RH arises naturally from the theory!
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
 An example of a hydrogenic
atom is He+ (Z=2)
 RH

RH
9

RH
4
 RH
 4 RH
THE SCHRÖDINGER EQUATION FOR THE
HYDROGEN ATOM CAN BE SOLVED EXACTLY
 Overall, the atomic orbitals require the specification of three quantum numbers:
n, l, ml.
 n = principal quantum number - energy.
 l = angular momentum quantum number - shape.
l=0
l=2
l=1
 ml = magnetic quantum number – direction.
ml=0
ml=+1
ml=-1
© ‘Chemical Structure and Reactivity: an Integrated Approach’, James Keeler and Peter Wothers, OUP 2008
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 ml.
n  1, 2, 3,....
l  0,1, 2,...(n  1)
ml  l , l  1, l  2...  l
l=0
l=1
l=2
l=3
l=4
s-orbital
p-orbital
d-orbital
f-orbital
g-orbital
 For hydrogenic atoms (i.e., one electron atoms), orbitals with
the same value of n are degenerate; i.e. of equal energy.
n  1, 2, 3,....
l  0,1, 2,...(n  1)
ml  l , l  1, l  2...  l
l=0
l=1
l=2
l=3
l=4
s-orbital
p-orbital
d-orbital
f-orbital
g-orbital
HYDROGENIC ATOMIC ORBITALS
The number of possible orbitals for a specified value of n is
equal to n2
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.
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 ml for 5p orbitals?
HYDROGENIC ATOMIC ORBITALS
© Atkins & Jones 2009
Self-Test: Complete the following table
n
1
5
3
6
4
l
0
3
1
0
2
ml values
Orbital name
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
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
BOUNDARY SURFACE
REPRESENTATIONS: 3d-ORBITALS
© ‘Chemical Structure and Reactivity: an Integrated Approach’, James Keeler and Peter Wothers, OUP 2008
BOUNDARY SURFACE
REPRESENTATIONS: 4f-ORBITALS
© ‘Chemical Structure and Reactivity: an Integrated Approach’, James Keeler and Peter Wothers, OUP 2008