28.THE ATOMIC STRUCTURE -Pauli’s exclusion principle,Afbau Principle,Hund’s rule of maximum multiplicity,Electronic Configurations.

The Nobel Prize for Chemistry this year is awarded to three great chemists namely,Jean-Pierre Sauvage(University of Strasbourg,France) ,Sir J. Fraser Stoddart(Northwestern University , USA) and Bernard L. Feringa (University of Groningen, the Netherlands)“for the design and synthesis of molecular machines” .They have developed world’s smallest machines – molecules with controllable movements.These can perform tasks when energy is added to them. These new developments will sure lead to new inventions and result in many technological advancements. Let us thank all the scientists and inventors who help make our lives better by harnessing the magic hidden within atoms!

So now coming back to atoms ….In the 19th century, this infinitesimal part of matter was revealing its secrets and scientists were going still deeper to find the world within this teeny tiny space. The revelations were mind-boggling and the complexity of structure was beyond imagination! Efforts to correlate the atomic structure with the classification of various elements gained momentum.With the advent of the concepts of four quantum numbers,sub shells etc, new questions were raised.How do electrons fill in these orbits? Is it a random event or is there a sequence / pattern to it? Along came many theories, four of which are the basis to our understanding of the periodic table today.These 4 theories  were as follows –

A] Pauli’s exclusion principle

200px-wolfgang_pauli_young
Wolfgang Pauli.

Wolfgang Pauli was a theoretical physicist and he enunciated a theory known as Pauli’s exclusion principle.It states –

“No two electrons can have the same set of four quantum numbers in an atom.”

For electron in the same orbital ,although the values of the quantum numbers n,ℓ and m remain the same, the value of spin quantum number differs.This is because if one electron in the orbital is moving in a clockwise direction the other has to move in anti-clockwise direction. Thus , one will have s= +1/2 and other will have s= -1/2.
e.g. In helium atom, there are two electrons in 1s shell.For both electrons , n=1,= 0 and m=0. But one of them has s= +1/2 (spin up – ↑ ) and one s= -1/2(spin down –  ↓) .

B] Afbau principle –

‘Afbau’is a German noun that means construction or “building-up“. This principle is not named after any scientist.It was formulated by Niels Bohr and Wolfgang Pauli. It explains how the electrons fill up in various shells and subshells. It states that ,

In an atom, the orbitals of lower energy get filled first with electrons and only then the subsequent higher energy orbitals are filled.

Thus, basically the electrons will always prefer to first enter a lower energy orbital.
e.g. 1s is lower energy than 2s orbital. So, in hydrogen atom , the electron will fill the 1s orbital.

C] Madelung (n+ℓ)  energy ordering rule –

In 1931,Erwin Madelung , a german physicist ,proposed empirical rule for filling of the orbitals by electrons.According to this rule,

‘The orbital with minimum (n+ℓ) value gets filled first by electrons’.

e.g . Let us consider 4s and 3d orbitals.

For 4s ,  (n+ℓ) = 4+0 = 4 (as ℓ = 0 for a s- orbital – as it has spherical shape)
For 3d ,  (n+ℓ) = 3+2 = 5 (as  ℓ = 2 for d-orbital).

Thus, the 4s orbital will be filled first by electrons.Thus, the order of filling of electrons in orbitals is 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d .

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D] Hund’s rule of multiplicity –

This rule throws light on whether or not electron pairing will occur in the same orbital. If there are two electrons of equal energies and we have two or more orbitals of same energies(called degenerate orbitals) , will the two electrons pair up in a single orbital or occupy different orbitals? One can think of it in terms of two benches in a garden. If two unknown people want to sit on those benches, will they both sit on the same bench or occupy different benches? the Hund’s rule of multiplicity states that,

The  electrons do not pair up in degenerate orbitals, until each orbital is first singly filled with parallel spin.

NOTE – AN ORBITAL CAN ACCOMODATE MAXIMUM OF TWO ELECTRONS ONLY.

So, orbitals of equivalent energy strive for unpaired electrons i.e they would prefer to have as many unpaired electyrons possible before the pairing starts.
e.g. – Nitrogen (Atomic number 7) has  three electrons in 2p orbital.

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Case 1 – the three electrons can occupy three different orbitals and thus not pair up.

OR

Case 2 – two electrons can pair up in a single orbital(one spin up and other spin down) and the third can later occupy the next orbital.

According to Hund’s rule of maximum multiplicity case 1 will be observed.

These developments helped immensely in correctly classifying elements and thus to the periodic table .The properties of elements could be studied based on how the electrons were distributed within the atom .This distribution of electrons was now called a the ‘electronic configuration’ of that element.

e.g. The  electronic configuration of Helium is 1s2 which indicates that there are 2 electrons in the s-orbital of the first shell.

The electronic configuration is the basis of everything we know today , as its this electronic configuration which dictates the properties of elements! The elctronic configuration of any element can be written by using the rules given above. These rules are fundamental to writing the electronic configuartions of elements and so they have to be studied well.

Question – Write the eleectronic configuration of carbon (Atomic number= 6).
Answer -1s2 , 2s2,2p2.

Practise writing the electronic configurations of various elements from the periodic table.The story of the atom doesnt end here .. it continues.. more on that in my next posts.Till then,

Be a perpetual student of life and keep learning…

Good day !

 

References and further reading –

1)https://www.nobelprize.org/nobel_prizes/chemistry/laureates/2016/press.html

2)https://en.wikipedia.org/wiki/Aufbau_principle

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