che10047 - electrons in atoms

8/18/2019 CHE10047 - Electrons in Atoms

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CHE-10047

CHEMICAL CONCEPTS AND STRUCTURE

2011-2012

Dr David J McGarvey

ELECTRONS IN ATOMS LECTURES 1-2


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Recall that we asked which of the following is the correctshape for allene?

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.

ALLENEC C C

H

HH

H

H2C C CH2

C C C

H

H

H

H

??

TOWARDS A MORE SOPHISTICATEDVIEW OF CHEMICAL BONDING

linear epg& mg

trigonal planarepg & mg


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An understanding of the electronic structure of atoms is

fundamental to a deeper understanding of the chemical andspectroscopic 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.

ELECTRONS IN ATOMS

Chapters 2, (11, 16) Chapter 1 Chapter 4


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Apply the Rydberg equation to predict the positions of spectral

lines for hydrogenic atoms.

Define and classify atomic orbitals in terms of the quantumnumbers (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.

LEARNING OUTCOMES


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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.

ELECTRONS IN ATOMS


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‘In classical systems (described by Newton’s laws) the positionof 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’.

TWO IMPORTANT FEATURESOF THE QUANTUM WORLD

© ‘Chemical Structure and Reactivity: an Integrated Approach’, James Keeler and Peter Wothers, OUP 2008


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‘In classical systems – which is what weexperience directly in our day-to-day lives –

energy can vary smoothly from one value to

another’.

‘In quantum systems, which applies to verysmall 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 neondischarge lamp.

TWO IMPORTANT FEATURESOF THE QUANTUM WORLD



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10/33http://jersey.uoregon.edu/vlab/elements/Elements.html

THE HYDROGEN ATOM SPECTRUM

http://jersey.uoregon.edu/vlab/elements/Elements.htmlhttp://jersey.uoregon.edu/vlab/elements/Elements.htmlhttp://jersey.uoregon.edu/vlab/elements/Elements.html


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The hydrogen atom consists of a proton and an electron.

The energy of the electron is restricted to certain values; i.e. itsenergy 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 toshells (e.g. the n = 1 shell).

The higher the value of n, the

higher the energy.

THE HYDROGEN ATOM

http://www.nobeliefs.com/atom.htm

http://www.nobeliefs.com/atom.htmhttp://www.nobeliefs.com/atom.htm


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THE ORIGIN OF EMISSION LINES INTHE HYDROGEN ATOM SPECTRUM

http://www.nobeliefs.com/atom.htm

n = 3→2 n = 4→2 n = 5→2

http://www.nobeliefs.com/atom.htmhttp://www.nobeliefs.com/atom.htm


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© Shriver & Atkins 2009

THE HYDROGEN ATOM SPECTRUM

Atomic spectroscopy forms the basis of some

exceptionally sensitive and selective analyticaltechniques (Atomic Absorption Spectroscopy (AAS),I nductively Coupled Plasma Atomic Emission

Spectroscopy (I CP-AES))


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ATOMIC SPECTRA, ENERGY LEVELS & LIGHT

hcc

hh E

c

1

When an electron in an atom undergoes a

transition from a higher energy level to alower one, it loses energy by emitting a

photon.


© Atkins and Jones 2005


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Self-Test: Calculate the energy (in kJ mol-1) associated with blue light of wavelength 400 nm.

Avogadro constant N A = 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


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upper U lower Lnn

RU L

H

22

11

1890: Rydberg noticed that all lines in the hydrogen atom emission spectrum

fit a general empirical equation.

THE HYDROGEN ATOM SPECTRUMAND THE RYDBERG EQUATION

© Atkins & Jones 2009

n L=2 n L=1

n L=3

n L=4

9

H R

4

H R

H R

© ‘Chemical Structure and Reactivity: an IntegratedApproach’, James Keeler and Peter Wothers, OUP 2008


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Self-Test: Calculate (in nm) for the transition from nU = 3 →n L = 2.

Rydberg constant R H = 1.09737 x 105 cm-1

upper U lower Lnn

RU L

H

22

11


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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.

THEORY AND EXPERIMENT


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The result is the following expression for the energy of the electronin the hydrogen atom:

We say that the energy is quantised and each energy level has anassociated quantum number, n, which affects its energy. The valueof the Rydberg constant R H arises naturally from the theory!

The key feature of the Schrödinger equation is its

solution, the wavefunction ().

For the electron in a hydrogen atom, thewavefunctions are known as atomic orbitals.

The atomic orbitals can only be viable (acceptable) if

the energy is quantised.

,...3,2,12 nn R E H n

THE SCHRÖDINGER EQUATION FOR THEHYDROGEN ATOM CAN BE SOLVED EXACTLY


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More generally, for hydrogenicatoms (an atom with 1electron) of atomic number Z,the energy of the electron in the

atom is given by:

An example of a hydrogenic

atom is He

+

( Z =2)

,...3,2,1

2

2

n

n

Z R E H n


9 H R

4

H R

H R

H R

H R4


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l =0 l =1 l =2

m l =0 m l =+1 m l =-1


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.

m l = magnetic quantum number – direction.


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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 .

l=0 s-orbital

l=1 p-orbitall=2 d-orbital

l=3 f-orbital

l=4 g-orbital

For hydrogenic atoms (i.e., one electron atoms), orbitals withthe same value of n are degenerate; i.e. of equal energy.

l l l l m

nl

n

l

...2,1,

)1,...(2,1,0

,....3,2,1


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l l l l mnl

n

l

...2,1,)1,...(2,1,0

,....3,2,1 l=0 s-orbitall=1 p-orbital

l=2 d-orbital

l=3 f-orbital

l=4 g-orbital


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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 onequantum number : n

i.e. for a hydrogenic atom, the energy of 2s = 2p and theenergy of 3s = 3p = 3d .


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Self-Test: How many orbitals are there with n=4? What orbitalscorrespond to (i) n=5, l=2, (ii) n=4, l=3? What are n, l and the

possible values of ml for 5p orbitals?


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Self-Test: Complete the following table

n l ml values Orbital name

1 05 3

3 1

6 0

4 2


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BOUNDARY SURFACEREPRESENTATIONS: 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.



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BOUNDARY SURFACEREPRESENTATIONS: 3p-ORBITALS

Notice that the general shape is similar to the 2p orbitals – see

later!



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BOUNDARY SURFACEREPRESENTATIONS: 3d-ORBITALS



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BOUNDARY SURFACEREPRESENTATIONS: 4f-ORBITALS



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che10047 - electrons in atoms

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