2.1b The modern
version of the Periodic Table is based on the electronic structure of
atoms

With our knowledge
of atomic structure the modern Periodic Table is now laid out in order of
atomic/proton number (Z) and any apparent anomalies sorted out.

The atomic/proton number of the nucleus
(Z) decides which element the
atom is, the number of electrons surrounding the nucleus of a neutral
atom and hence the element's chemistry
which is based on the electron configuration.

The
full Periodic Table (Z = 1 to 118) is shown
in section 2.4 with the element symbol, atomic/proton number (Z) and another
version of the
Periodic Table (Z = 1 to 56) showing
the electron configuration which is introduced and explained in the next
section 2.2.

Due to
isotopic mass variations and their nuclear stability, the relative atomic mass does
sometimes go 'up/down' as you proceed through the Periodic Table.

The use and
function of the Periodic Table will never cease! Newly 'man–made'
elements, beyond uranium (Z=92), are being 'synthesised' in nuclear reactors
and cyclotrons.
See
GCSE/IGCSE nuclear reactions
and radioactivity
pages

We now know the electronic structure of elements and can
understand how the electrons are arranged in principal and
sub–electronic levels and the 'quantum rules' of electron structure
are understood.

This knowledge now
allows us to understand why the Periodic Table makes sense in terms
of the known chemistry of the elements, and their subsequent
classification, prior to the discovery and understanding of the
significance of the sub–atomic particles, particularly the
proton and electron and their 'arrangement' in an atom.

Mendeleev and his
contemporaries central ideas on classifying elements, despite some
errors and omissions (i.e. not discovered), are now fully vindicated
by our knowledge of the electronic structure of atoms.

Mendeleev's
powerful intuition on 'element patterns' was brought to full
fruition by Rutherford and his contemporaries in discovering the
secrets of the atom and quantum physicists elucidating the 'quantum
patterns' of how multi–electron systems function.

For the simplified version of
expressing electronic arrangements up to atomic number 20 and the
relationship of the element in the Periodic Table, see the
GCSE/IGCSE Atomic Structure Notes.

Its not a bad idea to revise the
basics before getting stuck into the advanced stuff!

BUT, HOW DO WE GET TO THE MODERN
VIEW OF THE PERIODIC TABLE?  read on
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2.2
Orbitals and the electronic structure of the atoms
2.2a Types
of electron orbital and quantum numbers
The details
required by different pre–university syllabuses as regards background
theory and orbital knowledge seems to vary quite a lot, so I've done by
best to cater for all of them!
If you wish to go straight to working out the s, p,
d electron configuration of an element, click here!

How to use the advanced
s, p, d (f) notation for the electron configuration/arrangement of atoms/ions
is outlined below.

No knowledge of quantum mechanics is
required, but you do need to know how to work out electron
arrangements from the rules and a little knowledge of the shape of
orbitals wouldn't go amiss!

You do NOT need to know the origin of
the rules or know all about the four quantum numbers, BUT I can't
stand pulling rules out of a hat, so I have given a little
theoretical introduction.

To accurately
describe an electron in an atom requires four quantum numbers which
arise from solutions to the elaborate mathematical equations of quantum mechanics,
which describe the exceedingly complex wave behaviour of electrons.

These four quantum numbers
arise from solutions to the complex equations which describe the wave
and quantised behaviour of electrons surrounding the nucleus.

The first three
quantum numbers have 0 or +/– integer values and the fourth one is +/–
^{1}/_{2})

The Pauli
exclusion principle states that no electron in an atom can have the
same four quantum numbers,

The four
quantum numbers are:

The
principal quantum energy level
number n (n = 1,2, 3 ...), often just referred to as 'the
level or shell'. It is important to think of this as the principal
energy level, i.e. the principal quantum level an electron can
occupy.

The
subsidiary/azimuthal/angular quantum number, l, this defines the
'spatial' type
of sub–shell orbital, (l = 0 to n–1). often just
referred to as 'the sub–level or more specifically the
s/p/d/f sub–level' (see orbital diagrams later). Again, it is
important to think of this as a sub–energy level of an
electron.

For an s
orbital (l = 0), p orbital
(l = 1), d orbital (l = 2)
diagrams below, and
for the f orbital (l = 3).

For a
given principal quantum number the order of energy of the
sub–level is s < p < d < f.

The
magnetic
or spatial orientation quantum number,
m
(of the orbital),
in terms of x,y,z axis (m = –l ... 0 ... l)

where l
= the azimuthal quantum number 2. above and allows for each
principal quantum level n, one s orbital for n = 1, 2, 3 etc.,
three p orbitals per for n = 2, 3, 4 etc., 5 d orbitals for n
=3, 4, 5 etc. and seven orbitals for n = 4, 5, 6 etc.

See the
orientation of the three p type orbitals and the five d type
orbitals.

The
electron's spin quantum
number,
s,
which has the value of +^{1}/_{2} or –^{1}/_{2}^{
}and can be envisaged as the electron spinning
clockwise/anti–clockwise in an individual orbital.

Electrons
possess spin and if an orbital is filled then the pair of
electrons must have opposite spins (spin–paired).

This due to Pauli
exclusion principle, which states that no electron can have the
same four quantum numbers, since the other three quantum numbers
would be the same for a specific orbital, it is the spin quantum
number which will differ (+/– ^{1}/_{2}).

The principal
quantum electronic energy levels (n) can be split into sub–levels denoted
by s, b, d and f depending on the number of electrons in the
'system'.

The 'space' in
which the electron exists with its particular quantum level energy is
called the atomic orbital and each type, s, p, d or
f has its
own particular 'shape' or 'shapes' (see next section 2.2b).

Each individual atomic
orbital can 'hold' a maximum of two electrons.
2.2b s, p and d orbital
diagrams.

Orbital
diagram notes:

The diagrams are
NOT to scale and are somewhat simplified.

These are from
theoretical calculations based on the probability functions of the
peculiar behaviour of electrons from the deep realms of quantum
mechanics! Don't worry about it!

These mathematical
functions giving rise to an electron probability distribution e.g.
illustrated by the pictures below of s, p and d orbitals.

They only give a
very approximate representation of electron density.

Each orbital, that is the
space a particular quantum level occupies, can hold a maximum of two
electrons of opposite spin quantum number (+/– ^{1}/_{2})

Quantum physicists
would say that these picture are not real, its all matrix
mathematics really, BUT chemists like pictures, and pictures can
often help students understand difficult concepts and most
importantly, use the concepts to describe chemical systems and
predict properties of atoms and molecules etc.

s atomic orbital diagram

s orbitals
have a spherical shell shape and the faint dark blue circle represents
in cross–section, the region of maximum electron density.

Only one s orbital exists for
each principal quantum number denoted by 1s, 2s, 3s etc.

s sublevels have one orbital

*

p orbitals
diagram

p orbitals
are pairs of 'dumb–bells' aligned along the x, y and z axis at 90^{o}
to each other.

There are three p
orbitals for each principal quantum number from 2 onwards denoted by 2p,
3p and 4p etc.

e.g. 2p can be
composed of 2p_{x}, 2p_{y} and 2p_{z} if all
three orbitals for a particular principal quantum number are occupied.

If a p sub–shell is
full it holds a maximum of 3 x 2 = 6 electrons.

There is no 1p
because quantum rules do not allow this.

p sublevels have three orbitals

*

d
atomic orbital diagrams

d orbitals
have complex shapes, I say no more except their relative alignment is
important in explaining the origin of
colour in transition metal complexes.

There are five d
orbitals for each principal quantum number from 3 onwards denoted by 3d,
4d, 5d etc.

If a d sub–shell is
full it contains a maximum of 5 x 2 = 10 electrons.

There are no 1d or
2d quantum levels, the quantum rules do not permit these.

d sublevels have five orbitals

f orbitals
– orbital shapes not relevant at this level, the first is the 4f
level and there are 7 orbitals holding a maximum of 7 x 2 = 14
electrons if the sub–shell is full.
2.2c Working out and writing out the
electron configuration of an element

To sum up
'numerically' from the quantum
number rules, for the principal quantum number n ...

Each atomic
orbital can hold a maximum of two electrons.

For each
principal quantum level n, the following rules apply ...

for n = 1,
there is just
one sub–shell: 1s, maximum of 2 electrons,

for n = 2 there are two sub–shells: 1 x 2s atomic orbital and 3 x 2p orbitals, maximum of 2
+ 6 = 8 electrons,

for n
= 3 there are three sub–shells: 1 x 3s,3 x 3p
orbitals and 5 x 3d orbitals, maximum of 2 + 6 + 10 = 18 electrons,

for n
= 4 there are four sub–shells: 1 x 4s,3 x 4p
orbitals, 5 x 4d orbitals and 7 x 4f orbitals, maximum of 2 + 6 + 10
+ 14 = 32 electrons.

However the order of filling is not this simple (see below,
with visual diagrammatic help).

A summary of how many electrons
can occupy a particular level (first four principal quantum levels
only)

Principal quantum energy level 
type of quantum sublevel orbital 
maximum electrons in quantum sublevel 
maximum electrons in principal quantum level
or shell 
1 
s 
2 

2 
s 
2 
8 
p 
6 
3 
s 
2 
18 
p 
6 
d 
10 
4 
s 
2 
32 
p 
6 
d 
10 
f 
14 
 BUT, this is not necessarily the order in
which they are filled from principal quantum level 3 onwards, so beware
and read on!

How do we work out
electron the arrangement of an atom?

The arrangement of
electrons in the shells and orbitals is called the electronic
configuration or electron arrangement, electron structure or electron configuration and is
written out in a particular sequence.

sp d f orbital notation are used in
writing out electron configurations for chemical elements and their ions

The orbital
electrons are denoted in the form of e.g....

(i) 1s^{2}

means there are two electrons (super–script number
^{2})

in the s subshell orbital
(lower case letter)

and in the first principal quantum
level/shell (prefix number 1).

(ii) 2p^{3}

means there
are three electrons (super–script number ^{3})

in the p sub–shell orbitals (the lower case letter)

and in the second principal quantum
level/shell (prefix number 2).

(iii) 3d^{7}

means there
are seven electrons (super–script number ^{7})

in the d sub–shell orbitals (the lower case letter)

and in the third principal quantum
level/shell (prefix number 3).

(iv) 5f^{11}

means there
are eleven electrons (super–script number ^{11})

in the f sub–shell orbitals (the lower case letter)

and in the 5th principal quantum
level/shell (prefix number 5).



The quantum
levels and associated orbitals are filled according to the
Aufbau
Principle which states that an electron goes into the lowest available
energy level providing the following 'sub–rules' are obeyed.

The Pauli exclusion principle
states that no two electrons can have the same four quantum numbers.

Hund's Rule of
maximum multiplicity states that, as far as is possible, electrons will
occupy orbitals so that they have parallel spins.

This means if a set of
sub–shell orbitals of the same energy level e.g. for a 2p or 3d set, each
orbital will be singly occupied before pairing (to minimise electron
repulsion within a single atomic orbital, i.e. a lower energy state than
paired electron orbitals and unoccupied orbitals.

The orbitals are
filled in a definite order to produce the system of lowest energy and
any electron will go into the lowest available energy level before
filling a higher level orbital.

This is known as the aufbau
principle.

The order of 'filling'
for an electron configuration is shown in the diagram below.

It uses is
a simple diagrammatic
convention to show an atomic orbital as a 'spin' box.

Electrons are
shown as
half–arrows (up/down to represent the different spin quantum number s),
see the 2nd diagram.


A note on the 'spin boxes'
representing subshell orbitals:

and
would represent a singly and doubly occupied s orbital.

would represent three empty p subshell orbitals, referred to as
vacant orbitals.

would represent two halffilled p orbitals.

would represent three full p subshell orbitals.

would represent five empty d orbitals of a particular d subshell.

would represent three halffilled d orbitals and two vacant.

would represent three completely filled d orbitals and tow halffilled.

would represent five completely filled d orbitals of a particular d
subshell

I've used this style of diagram on
the next page were the electron configurations of elements 1 to 58 are
listed.

The order of
filling (up to atomic number Z = 36, H to Kr) is
1s 2s 2p 3s 3p
4s 3d 4p ...

... up to a total 36 electrons from Z = 1 to 36 i.e. the
order of increasing energy of the subshell or energy sub–level.

Note the 'quantum quirk' in order for
filling the 3d sub–shell energy level (see
also the diagram below).

Until atomic number 21 (Sc) is reached, the
3d level is too high in energy and the electrons go into the 4s level
and then the 3d level is filled from Sc to Zn.

This, and
other 'quirks' I'm afraid, are a feature of the quantum
complexity of multi–electron systems, so just learn the rules
and get on with life!

After Z=30, the 'filling' of
the 4p level begins with Ga (Z=31) and finishes with Kr (Z=36).

After Z=36, and up to Z=56,
so after 4p the
filling order is, 5s 4d 5p 6s, thus completing period and starting
period 6 (and also repeating the pattern of filling in period 4
including a 2nd block of metals, the 4d block.


Above is the electron spin box
diagram showing all the empty levels available from 1s to 6s.

Shown below are various electron
spin box diagrams derived from the above diagram and employing the
Aufbau principle and Pauli's exclusion principle and Hund's rule to
give the full electron configuration of the element.

carbon (Z = 6) 1s^{2}2s^{2}2p^{2} (group 4/14
element)

neon (Z = 10) 1s^{2}2s^{2}2p^{6} (group 0/8/18
noble gas element)

silicon (Z = 14) 1s^{2}2s^{2}2p^{6}3s^{2}3p^{2}
(group 4/14 element)

argon (Z = 18) 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}
(group 0/8/18 noble gas element)

calcium (Z = 18) 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}
(group 2 metal element)

vanadium (Z=23)
1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{3}4s^{2}
(3d block transition metal, now considered the top element in group
15)

For just a thought
experiment, do the following ...

'Empty' the 3d
level of electron arrows and you get the diagram for calcium (Z = 20).

Fill up
completely the
3d and 4p boxes with arrows and you get krypton (Z = 36)

and learn to fill in anything
in between!

The
table in Part 2.3 shows how
they are written out up to Z = 56 and a few others and note the orbital order when
writing out.

They are
written out in strict order of principal quantum number 1, 2, 3 etc. and each
principal quantum number is followed
by the s, p or d sub–levels etc., and this is irrespective of
the order of filling, i.e. when writing out the configuration, you
ignore the 3d filling 'quirk' described above.

Also in the table,
some
are written out in box diagram format, each box represents an orbital
with a maximum of two electrons of opposite spin (shown by the
opposing arrows).

Elements with one
or two outer s electrons, and no outer p or d electrons etc., are called
s–block
elements (Groups 1 & 2). 
Elements with at least one outer p electron
are called p–block elements (Groups 3 to 0/8, modern notation
Groups 13 to 18).

Elements where the
lowest available d
sub–shell is being filled are called d–block elements (*Transition
Metals) and similarly elements where the lowest available f sub–shell is being filled are called
f–block elements (the Lanthanides and Actinides).

Sc–Zn is the 3d
block, BUT, in terms of definition, true transition elements form at least one chemically
stable ion with a
partly filled sub–shell of d electrons.

Sc
only forms Sc^{3+} [Ar]3d^{0}, and Zn only forms
Zn^{2+} [Ar]3d^{10}4s^{2}, so the
true 3d–block transition metals are from Ti to Cu.

Can you spot the other electronic
'quirks' for chromium and copper?

Explanation:
It would appear that a half–filled 3d subshell (Cr) or a full 3d
sub–shell (Cu) is a tad more stable than a full 4s level.

Quantum theory dictates
that electrons can only have certain specific 'quantised' energies and any
electronic level change requires a specific energy change i.e. energy
quanta absorbed or energy quanta emitted.

Any electron will occupy
the lowest available energy level according to the
Aufbau principle (previously described).

The order of 'filling' up
to atomic number 56 from the lowest to highest quantum level is thus ...

Writing out electron
configurations for atoms

BUT first, how to
work out the electron arrangement from the atomic/proton number,

AND then how to write
out the electron configuration.

To work out an
electron arrangement for an atom, you start with the atomic number
(Z), then
'fill in' the levels and sub–levels according to the rule.

Example 1. sodium,
Na, Z = 11

1s filled (2e) 9e's
left, 2s filled (2e's) 7e left, 2p filled (6e's) 1e left, last electron goes into
the 3s level.

According to the notation rule this is written as ...

1s^{2}2s^{2}2p^{6}3s^{1}
(2.8.1 in simplified shell notation)

This can be shortened to:
[Ne]3s^{1}

Example 2. vanadium,
V, Z = 23

1s filled (2e's) 21e's
left, 2s filled (2e's) 19e left, 2p filled (6e's) 13e's left, 3s filled (2e's)
11e's left, 3p filled (6e's) 5e's left, 4s filled (2e's) 3e's left, last 3e's go
into 3d level.

According to the notation rule this is written as ...

1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{3}4s^{2}
(2.8.11.2 in simplified shell notation


Example 3. bromine,
Br, Z = 35

Filling in the first
18e's as described
in example 2. will give an argon structure (1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}),
which can be abbreviated to [Ar], the next 2e's go into the 4s level (15e's
left), the next 10e's go into the 3d level, the final 5e's go into the 4p
level.

[Ar]3d^{10}4s^{2}4p^{5}
(2.8.18.7 in simplified notation, but do NOT try to simplify the s, p
and d version)

Note the use of 'noble gas notation' as an abbreviation for all the
filled inner sub–shells making up the equivalent of noble gas electron
arrangement, and will not include the 'outer electrons').
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revision study notes for AQA Edexcel OCR Salters advanced
A level chemistry on s p d and f electron orbitals, explaining quantum
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Table is based on the electronic structure of atoms, describing and
explaining the types of electron orbital and quantum numbers, how
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