the periodic table - university of sussex€¦ · the definition of the periodic table 3. aspects...

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THE UNIVERSITY OF TENNESSEE

KNOXVILLE

KNOX COUNTY SCHOOLS 13TH FEBRUARY 2004

The Periodic Table

John F. C. Turner

Department of Chemistry and

Neutron Sciences Consortium

The University of TennesseeKnoxville

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Structure

1. Misconceptions about the Periodic Table

2. The definition of the Periodic Table

3. Aspects of the periodicity of the elements

4. Summary

5. Questions

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Misconceptions

It is hard

It has no rule

It is unstructured

It is a barrier that can only be overcome by the brilliant or the odd

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The Definition of the Periodic Table

An array of the elements in increasing atomic number or atomic mass, grouped according to chemical property

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The Beginnings of the Periodic Table

In antiquity, prior to ~1800 only 15 – 20 elements were known;

By 1860, ~60 were isolated – enough for trends to be apparent

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The Beginnings of the Periodic Table

Most importantly, different members of the same chemical family were isolated – the groups.

Li, Na, K,

Be, Mg, Ca, Sr,

showing similar but not identical properties

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Periodic physical properties

1. The majority of the elements are metals. A metal is defined as

a material whose electrical conductivitydecreases with temperature

This is obscure and is determined by the manner in which the electrons are bound in the substance

This leads to other properties that are more intuitively obvious

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Non-metals and metals

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Periodic physical propertiesMetals are

� Good conductors of heat and electricity� Malleable and ductile� Highly reflective� Opaque to visible light� Chemistry is dominated by the formation of

cations – loss of electrons

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Non-metals are � Poor conductors of heat and electricity� Brittle� Chemistry is dominated by the formation of

anions – gain of electrons

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Solids, liquids and gases

Strong correlation between Metals Solids

Non-metals Gases

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These are bulk properties and do not explain the chemical periodicity and therefore the periodicity of the table

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Observed Periodicity in the physical properties

Melting points

Boiling points

Liquid range

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Observed Periodicity in the physical properties

The forces between particles are roughly the same in both the liquid and the solid

Periodicity in seen in the melting point, the boiling point and the liquid range

This phenomenon is independent of the phase of matter we are discussing

It is more fundamentalIt is atomic

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However, the bulk properties and the microscopic properties must be related.

What are the trends in the ionization energy?

A � e- � A + ionization energy

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Periodicity of the ionization energyAcross the row, it becomes increasingly difficult to remove an electron(chemical energy scale: ~0 - ~10 eV)

Electrons are more tightly bound and therefore the atom is smaller across the table

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The structure of the atom and the Periodic Table

Problems with the atom:

It is a quantum system.

What is a quantum system?

One that is small on an absolute scale

What is “small on an absolute scale”

That is a good question.............

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“Newtonian world”

We live in a material, macroscopic world, where all energies are allowed and everything moves in a trajectory

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“Quantum world”

Objects are profoundly affected by the physics of observation.

No trajectories No positions No velocity

A large object is one that is perceptibly unaffected by measurement

A small object is one that is affected by measurement

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The atom is a quantum system.

De Broglie relationship relates themotion of a particle to wave-like properties and the electron in an atom behaves as a wave.

Standing waves have fixed energies

violin stringsorgan pipeselectrons in atoms

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The atom is spherical and there are three important coordinates

The distance between the electron and the nucleus

The 'longitude'

The 'latitude'

The electron-wave is defined by all three coordinates.

Each coordinate of the electron-wave has a label attached to it – the quantum number.

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The gross energy of the atom is dominated by the radial quantum number, n.The larger n, the larger the atom

large n

small n

n

n corresponds to the period number in the table

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Within each n value, there are two other labels – the longitude and the latitude

These are associated with angular motion – the circulation of the electron around the nucleus.

These quantum numbers apply to the number of groups – the s block, the p block, the d block and the f block.

s block

n

p block

d block

f block

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The angular quantum number, l, gives

Block l value s 0 p 1 d 2 f 3The circulation of the electron in the s block

is the smallest, 1 unit, larger in the p and so on.

s block

n

p block

d block

f block

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Angular momentum and the Periodic table

The angular momenta associated with the latitude and the longitude are linked.

For any value of l there are (2l+1) values of ml

Thus:

l ml

s block 0 1p block 1 3d block 2 5f block 3 7

and so on.

The ml

value can be interpreted as the

orientation of the longitudinal circulation in space.

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Angular momentum and the Periodic table

Givenl m

l

s block 0 1p block 1 3d block 2 5f block 3 7

We should expect 1 electron in each of the m

l quantum numbers and therefore

1 s block element per period3 p block elements per period5 d block elements per period7 f block elements per period

Instead, there are 2, 6, 10 and 14 elements?

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The rules of angular momentum

The final part of the structure of the Periodic Table is determined by the rules of angular momentum

'The rules of angular momentum' describe a whole range of different behaviors; they are difficult to present as their basis is very abstract.

However, they cover the properties of any body in motion and so are extremely important.

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The rules of angular momentum

The generalities of angular momentum are classically derived from the vector cross product together with the applications of the theory of symmetry.

Quantum mechanical angular momentum obeys the same type of rules, but translated into the quantum world.

The quantum rules are:

For every value of the angular momentum l,quantum number, thereare 2l+1 orientations, with m

l = -l....0....l

in single unit steps.

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The electron possesses an intrinsic angular momentum, s= ½ and therefore the two possible orientations are labeled as

ms = + ½ or - ½

The quantum labels for any electron are

Principle Angular Electron

radius, r Longitude Latitude spin

n l ml s

then four quantum numbers define the behavior of the electron in the atom.

3 space �nl

ml� 1 spin � s �

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Each electron in an atom is unique and its behavior is defined by the four quantum numbers.

All four must be different and therefore for each set of spatial quantum numbers, {n, l, m

l}, we

have the choice of ms = + ½ or - ½

- two choices per {n, l, ml} set.

The numbers of the elements that are available are therefore:

l ml

ms

s block 0 1 2p block 1 3 6d block 2 5 10f block 3 7 14

as required.

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The Periodic table and the atom

The structure of the periodic table is determined in a gross manner by the atomic properties of the atoms

The precise details are not as quantitative as the description of the overall structure for several reasons.

� Electrons interact with the nucleus as well as with other electrons – an example of a many body problem

� These interactions are increasingly important as the atom becomes larger

Several trends can be identified.

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The Periodic table and the atom

As the atom becomes larger, the electrons become less strongly bound.

Stronger bonds are formed between smaller atoms.

Atomic size

increases down the group for a given group

decreases across the period with increasing atomic number

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Summary

Periodicity is seen in the Periodic Table whenever a property is based on an atomic property of some description

It is a powerful tool with which to introduce concepts important in the description of the atomic nature of the microscopic world

It is not immensely complex, but is more easily understood through the fundamental concepts that produce the structure, rather than starting with the structure.

Acknowledgments

Dr. Lynn ChampionDr. Charmaine Mamantov

the periodic table - university of sussex€¦ · the definition of the periodic table 3. aspects...

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