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.

  • In these notes the convention Z = atomic/proton number is used extensively, its a handy shorthand.

• 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.

  • See Part 1 Mendeleev's Periodic table work.

• 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,

  • i.e. at least one must differ from electron to electron for the electronic energy levels of a specific single atom.

• The four quantum numbers are:

  1. 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.

  2. 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.

  3. 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.

  4. 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:

  1. The diagrams are NOT to scale and are somewhat simplified.

  2. 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!

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

  4. They only give a very approximate representation of electron density.

  5. 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)

  6. 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 sub-levels 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 sub-levels 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 sub-levels 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.

  • f sub-levels have seven orbitals (no details needed pre-university!)

• Don't worry too much about all the 'quantum' details above, the important features to appreciate are described below.

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 sub-level orbital	maximum electrons in quantum sub-level	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?

  • and how to use the orbital notation to write out the full electron configuration of an element or its ion?

• 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) 1s²

    • means there are two electrons (super–script number ²)

    • in the s sub-shell orbital (lower case letter)

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

  • (ii) 2p³

    • 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) 3d⁷

    • 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) 5f¹¹

    • 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 sub-shell orbitals:

    • and would represent a singly and doubly occupied s orbital.

    • would represent three empty p sub-shell orbitals, referred to as vacant orbitals.

    • would represent two half-filled p orbitals.

    • would represent three full p sub-shell orbitals.

    • would represent five empty d orbitals of a particular d sub-shell.

    • would represent three half-filled d orbitals and two vacant.

    • would represent three completely filled d orbitals and tow half-filled.

    • would represent five completely filled d orbitals of a particular d sub-shell

    • 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) 1s²2s²2p² (group 4/14 element)

  • neon (Z = 10) 1s²2s²2p⁶ (group 0/8/18 noble gas element)

  • silicon (Z = 14) 1s²2s²2p⁶3s²3p² (group 4/14 element)

  • argon (Z = 18) 1s²2s²2p⁶3s²3p⁶ (group 0/8/18 noble gas element)

  • calcium (Z = 18) 1s²2s²2p⁶3s²3p⁶4s² (group 2 metal element)

  • vanadium (Z=23) 1s²2s²2p⁶3s²3p⁶3d³4s² (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).

  • Note the electrons only pair up when all sub–orbitals are filled separately with a single electron (this minimises electron pair repulsion within an orbital).

• 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 Sc³⁺ [Ar]3d⁰, and Zn only forms Zn²⁺ [Ar]3d¹⁰4s², 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 ...

  • 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s

• 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.

  • The electron configuration is written out in order of,

    • firstly, the principal quantum energy level

    • then within this level in s, p, d, f order

    • and the total number of electrons in each sub–energy level is shown as a super–script.

    • You can use [noble gas] as a shorthand notation, but beware in an exam question that might ask for the fully written out electron configuration.

  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 ...

  1s²2s²2p⁶3s¹  (2.8.1 in simplified shell notation)

  This can be shortened to: [Ne]3s¹

  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 ...

  1s²2s²2p⁶3s²3p⁶3d³4s²  (2.8.11.2 in simplified shell notation

  • This can be shortened to: [Ar]3d³4s²

• Example 3. bromine, Br, Z = 35

  Filling in the first 18e's as described in example 2. will give an argon structure (1s²2s²2p⁶3s²3p⁶), 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]3d¹⁰4s²4p⁵  (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').

---

WHAT NEXT? PLEASE NOTE GCSE Level periodic table notes are on separate webpages Advanced inorganic chemistry Part 2 sub-index: 2.1 The electronic basis of the modern Periodic Table * 2.2 The electronic structure of atoms (including s p d f subshells/orbitals/notation) * 2.3 Electron configurations of elements (Z = 1 to 56) * 2.4 Electron configuration and the Periodic Table * 2.5 Electron configuration of ions and oxidation states * 2.6 Spectroscopy and the hydrogen spectrum * 2.7 Evidence of quantum levels from ionisation energies * 2.8 Emission and absorption spectra of elements Advanced Level Inorganic Chemistry Periodic Table Index: Part 1 Periodic Table history Part 2 Electron configurations, spectroscopy, hydrogen spectrum, ionisation energies * Part 3 Period 1 survey H to He * Part 4 Period 2 survey Li to Ne * Part 5 Period 3 survey Na to Ar * Part 6 Period 4 survey K to Kr AND important trends down a group * Part 7 s–block Groups 1/2 Alkali Metals/Alkaline Earth Metals * Part 8  p–block Groups 3/13 to 0/18 * Part 9 Group 7/17 The Halogens * Part 10 3d block elements & Transition Metal Series * Part 11 Group & Series data & periodicity plots All 11 Parts have their own sub-indexes near the top of the pages Group numbering and the modern periodic table The original group numbers of the periodic table ran from group 1 alkali metals to group 0 noble gases (= group 8). To account for the d block elements and their 'vertical' similarities, in the modern periodic table, groups 3 to group 0/8 are numbered 13 to 18. So, the p block elements are referred to as groups 13 to group 18 at a higher academic level, though the group 3 to 0/8 notation is still used, but usually at a lower academic level. The 3d block elements (Sc to Zn) are now considered the head (top) elements of groups 3 to 12.

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keywords and phrases: revision study notes for AQA Edexcel OCR Salters advanced A level chemistry on s p d and f electron orbitals, explaining quantum energy levels and sub–shells and how modern version of the Periodic Table is based on the electronic structure of atoms, describing and explaining  the types of electron orbital and quantum numbers, how to draw p and d orbital diagrams, How to write and work out the electron configuration of an element using the aufbau principles rules, Hund's rule and Pauli's exclusion principle, lots of examples explained, drawn diagrams and written out, explaining the order of filling the s, p, d and f orbitals to obtain the electron configuration of an element

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