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Draw structure of d-subshell with explanation.

*

  d atomic orbitals

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.

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.

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

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).

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/structure and is written out in a particular sequence.

The orbital electrons are denoted in the form of e.g. 2p3

means there are three electrons (super-script number 3)

in the p sub-shell (the lower case letter)

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

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. 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.

 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 box.

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

 

 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 sub-shell or energy sub-level.

Note the '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.

The diagram for vanadium (Z=23), 1s22s22p63s23p63d34s2 is shown below.

  *

 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)

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 and 2).

Elements with at least one outer p electron are called p-block elements (Groups 3 to 8/0).

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

* Sc-Zn is the 3d block, BUT 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.

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 ...

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

Writing out electron configurations for atoms:

To work out an electron arrangement for an atom, you start with the atomic number, 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.

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)

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)

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)

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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