part one - the structure of atoms

8/10/2019 Part One - The Structure of Atoms

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The structure of atoms.

What will be covered?

1.

The nucleus

2.

Atomic weight

3.

Electronic structure

4.

Electronic configuration of the elements

5.

Valence

6.

Hybridization

7.

Periodic table

Why do we need to know this material?

Atomic structure is the foundation of Materials Science.

This material will form the basis for understanding the interatomic and

intermolecular forces to be covered in the next section.

Fundamentals.

Atoms consist of nuclei and electrons.

Nuclei are composed of protons and neutrons.

Protons carry a positive charge of 1.69x10-19coulombs and have a mass

at rest of 1.67x10-24 g.

Neutrons have no charge and have the same rest mass as protons.

Overall the nucleus is thus positively charged.

This charge is balanced by an equal charge due to a number of electrons

equal to the number of protons (for neutral atoms).

Each electron carries a charge of 1.69x10-19coulombs.

Nucleus.

The number of protons in the nucleus is called the atomic number (this

defines the elemental identity).


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The number of neutrons in a nucleus is larger than or equal to the number

of protons, with the larger excess of neutrons occurring for the larger

atomic numbers.

Many elements have isotopes, i.e. their nuclei contain an equal number of

protons but have different numbers of neutrons; some of these isotopes

are stable while others decompose via radioactive decay.

Atomic weight.

The atomic weight is given in terms of atomic mass units (amu) and

indicates the mass of the atom in units of 1/12 the mass of the carbon

isotope with 6 protons and 6 neutrons.

The isotope therefore has an arbitrary atomic weight of 12 amu and is

represented as 6C12.

Here the subscript is the atomic number and the superscript the mass

number, i.e. the sum of the number of protons and neutrons.

Atomic weights are not whole numbers except for C12by definition.

The actual masses of the nuclei are not equal to the sum of the masses of

all protons and neutrons but differ from that sum by the binding energy

expresses as mass according to E=mc2

.

Atomic weights are normally weighted according to the natural

abundance of the isotopes.

For elements with large atomic masses, the binding energy is such that if

an atom is split, the sum of the binding energies of the two resulting

smaller nuclei is smaller than that of the parent nucleus.

The difference is liberated as energy (fission).

For the case of elements with small atomic masses such as hydrogen,

energy is liberated when nuclei are fused (fusion).

Electronic structure.

From a basic materials science point of view, the arrangement of the

electrons is the most important aspect of atomic structure.


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The electronic structure determines the type and strength of the chemical

bonds that can be established with other atoms and hence determines

many important materials properties.

For our purpose, we can consider electrons as particles, which surround

the nucleus in some particular fashion such that their number is equal to

the atomic number of the element (for neutral atoms).

Example: the carbon atom: outside the nucleus it has six electrons. Using

the Bohr theory of atomic structure, these were believed to be arranged

in orbits of increasing distance from the nucleus. These orbits

corresponded to gradually increasing levels of energy, that of the lowest

energy, the 1s, accommodating two electrons, the next 2s, also

accommodating two electrons and the remaining two electrons of thecarbon atom going into the 2p level, which is actually capable of

accommodating a total of six electrons.

The Heisenberg uncertainty principle and the wave mechanical view of

the electron have made it necessary to do away with anything so

precisely defined as actual orbits. Instead, the wave-like electrons are

now symbolized by wave functions such that the precise classical orbitals

of Bohr are superceded by three-dimensional atomic orbitals of differing

energy level.

Thus, from quantum theory it can be established that electrons have

different energies; discrete electron energy levels can be described in

terms of quantum numbers.


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Schrdinger Wave Equation (SWE):

where h is Planks constant, m is the particle mass, V(x,y,z) is the potential

energy, and (x,y,z,t) is the wave function.

Solutions to the SWE generate four quantum numbers.

There is a principal quantum number (n), which can assume only integer

values (n = 1,2,3,4).

Each of these numbers designates a shell around the atom in which

certain electrons exist.

Generally, the larger the value of n, the larger the energy of the electron

in that shell.

Within each shell the electrons carry a further quantum number (I).

This azimuthal quantum number is associated with the total orbital angular

momentum and can assume values from 0 to n-1.

As a rule, energy increases with increasing I(although there are

exceptions).

The shells are further subdivided by the magnetic quantum number mIare

1.

Finally, a fourth quantum number (s) which takes into account theelectron spin direction is assigned values of 1/2.

In order to develop a simple model of electron distribution in the elements

we must take into account the Pauli exclusion principle: only one electron

can be in a particular quantum state at a particular time, i.e. no two

electrons can have identical values of the four quantum numbers.

The maximum number of electrons that can exist in each shell is given by

2n2.


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The maximum number of electrons that can occupy the 1 subshell is

2(2I+1).

An alternate scheme is often used to indicate the electron quantum

values in terms of capital letter for the principal quantum numbers

(K,L,M,) and lower case letters for the azimuthal quantum numbers (s, p,

d and f).


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Electronic configuration of the elements.

The electrons of an atom are generally assigned spaces in shells and

subshells according to increasing energy.

As a rule, this is in order of increasing n, and within n in order of increasing

I.

There are important exceptions to this scheme.

The energy of the typical 4sshell is lower than the energy of the 3dshell;

similarly, the energy of the typical 5sshell is lower than the energy of the

4dshell.

Therefore, thesshells are filled before the d shells with the lower main

quantum number.

This has important consequences regarding the magnetic properties of

the affected elements.


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Valence.

This is related to the ability of the atom to enter into the chemical

combination with other elements, i.e. atomic bonding.

Valence is often determined by the number of electrons in the outermost

combinedsplevel.

Thesespelectrons may be added to, lost or shared with other atoms thus

determining the nature of the atomic bonds.

The ground state of the carbon atom will be: 1s22s22px12py1with the 2pz

orbital unoccupied. The two unpaired electrons are available for the

formation of bonds with other atoms and at first sight appears divalentwhereas the majority of stable compounds appear as quadrivalency. The

2s2is therefore uncoupled to give 1s22s12px12py12pz1.

Hybridization.

A carbon atom combining with four other atoms clearly does not use the

one 2s and the thre 2p atomic orbitals that would now be available for

this would lead to the formation of three directed bonds, mutually at right

angles to one another (with the three 2p orbitals), and one different, non-

directed bond (with the spherical 2s orbital). Whereas in fact, the four C-Hbonds in, for example, methane (CH4) are known to be identical and

symmetrically (tetrahedrally) disposed at an angle of 109o28 to each

other. This may be accounted for on the basis of re-deploying the 2s and

the three 2p atomic obitals so as to yield four new (identical) orbitals,

which are capable of forming stronger bonds. These new orbitals are

known as sp3hybrid atomic orbitals, and the process by which they are

formed is known as hybridization.

When a carbon combines with three other atoms (e.g. ethylene, C2H4) we

have three sp2 hybrid atomic orbitals disposed at 120oto each other in

the same plane (plane trigonal hybridization).

When a carbon atom combines with two other atoms (e.g. acetylene,

C2H2), two sp1 hybrid atomic orbitals disposed 180o to each other

(digonal hybridization) are formed. In each case the s orbital is always

involved as it is the one of lowest energy.

Hybridization takes place so that the atom concerned can form as strong

a bond as possible, and so that the atoms thus bonded (and the electron

pairs constituting the bonds) are as far apart from each other as possible


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to ensure that the total intrinsic energy of the resultant compound is at a

minimum.

Periodic table of the elements.

Based upon their electronic configurations, the elements can be sensibly

ordered in an arrangement known as the periodic table.

The chemical character of an element is controlled by its atomic number

and by the configuration of the outermost electrons.

The electronic arrangement determines the group (vertical columns) into

which the element will fall whereas the atomic number determines theposition within this group.

Columns refer to the number of electrons present in the outermostsp

energy level and correspond to the most common valence.

Horizontal rows are called periods and correspond to the value of the

principal quantum numbers.

Arranged in this way, there is a certain similarity of the chemical properties

of the elements in a group as well as a systematic variation across aperiod.

Some groups of elements are given certain names to emphasize their

chemical similarity:

Group IA: alkali metals

Group IIA: alkaline earth metals

Group VIIA: halogens

Group O: noble gases

Electronegativity of the elements increases progressively from left to right

and bottom to top.

Metals are electropositive whereas non-metals are electronegative.

Classification according to 16 non-metals, 6 intermediates and the

balance as metals.


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part one - the structure of atoms

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