Aufbau principle and Bohr Bury rule

The distribution of electrons in different orbitals is known as its electronic configuration. This characterizes each electron in an atom. The electronic configuration is expressed by indicating the principal quantum number and its respective orbital along with the number of electrons present in it. For example the notation 3p_x¹ indicates that in the third principal shell there is one electron in the 'p_x' orbital.

Sometimes the electronic configuration is also described by box notation form i.e., putting an arrow for single electron in a box or a pair of arrows for two electrons in a box. The direction of the arrows gives the orientation of its spin.

Further the box is labelled on top by writing the symbol of the orbital.

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Rules for Filling the Orbitals

Aufbau principle

The principle states that the electron in an atom are so arranged that they occupy orbitals in the order of their increasing energy. Since the energy of a 'n' orbital in the absence of any magnetic field depends on the 'n' and 'l' quantum number values, the order of filling orbitals with electrons may be obtained from the (n + l) rule of Bohr Bury's rule.

According to this principle the orbital with the lowest energy will be filled first. The orbital having lower (n + l) value has lower energy. However for orbitals whose (n + l) values are equal, the orbital having lower value of 'n' has lower energy. It is important to remember that because of this rule, this sequence of energy levels pertains to energy level up to '3p' and thereafter, '4s' orbitals comes first instead of '3d'. Thus, the orbitals should be filled in the order:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s

Fig: 3.19 - A simple way to determine the relative energies of different orbitals

Bohr Bury rule

Electrons revolve around the nucleus in different energy levels or shells and each shell is associated with definite energy. The energy of the K shell is the least while those of L, M, N and O shells increases progressively. We also know that any system that has least energy is the most stable.

1^st energy level is K shell

2^nd energy level is L shell

3^rd energy level is M shell

4^th energy level is N shell and so on.

Electronic configuration of an element

The arrangement of electrons in the various shells/orbits/energy levels of an atom of the element is known as electronic configuration.

Bohr and Bury Scheme - Important Rules

• Maximum number of electrons that can be accommodated in a shell is given by 2n² where n=shell number

• For 1^st energy level, n = 1

Maximum number of electrons in 1^st energy level = 2n²

2 x (1) 2 = 2

• For 2^nd energy level n=2

Maximum number of electrons in the 2^nd energy level = 2n²

2 x 2² = 2 x 4 = 8

• For 3^rd energy level n=3

Maximum number of electrons in the 3^rd energy level = 2n²

= 2x(3)²

= 2x9=18

• For 4^th energy level n=4

Maximum no.of electrons in the 4^th energy level = 2n²

= 2x(4)²

= 2x16=32

Sl No.	Electron Shell	Maximum capacity
1.	K Shell	2 electrons
2.	L Shell	8 electrons
3.	M Shell	18 electrons
4.	N Shell	32 electrons

• The outermost shell of an atom cannot accommodate more than 8 electrons, even if it has a capacity to accommodate more electrons. This is a very important rule and is also called the Octet rule. The presence of 8 electrons in the outermost shell makes the atom very stable.

Keeping these points in mind let us write the electronic configuration of elements.

Electronic configurations of some important elements

Element	Symbol	Atomic number	Electronic configuration (or Electron arrangement) KLMN
Hydrogen	H	1	1
Helium	He	2	2
Lithium	Li	3	2,1
Beryllium	Be	4	2,2
Boron	B	5	2,3
Carbon	C	6	2,4
Nitrogen	N	7	2,5
Oxygen	O	8	2,6
Fluorine	F	9	2,7
Neon	Ne	10	2,8
Sodium	Na	11	2,8,1
Magnesium	Mg	12	2,8,2
Aluminium	Al	13	2,8,3
Silicon	Si	14	2,8,4
Phosphorus	P	15	2,8,5
Sulphur	S	16	2,8,6
Chlorine	Cl	17	2,8,7
Argon	Ar	18	2,8,8
Potassium	K	19	2,8,8,1
Calcium	Ca	20	2,8,8,2

Geometric Representation of Atomic Structure

Example:

Steps:

• The first 2 electrons will go to the 1^st shell = K Shell (2n²)

• The next shell L takes a maximum of 8 electrons (2n²).

• In this way 2 + 8 = 10 electrons have been accommodated. The next 2 electrons go to the M Shell.

K L M
2,8,2

Example

Special case of potassium and calcium elements

Atomic number of potassium is 19 and its electronic configuration is

K L M N
1 8 8 1

Atomic number of calcium is 20 and its electronic configuration is

K L M N
2 8 8 2

This abnormal behaviour can be explained as follows:

It is found that shells have sub shells. The smaller sub shells are termed s, p, d and f. The maximum number of electrons that can go into these are 2, 5, 10 and 14 respectively. These sub shells can overlap, resulting in energies that may differ from that predicted purely on the basis of n=1, 2, 3 etc. Therefore when electrons start filling, they may go to a new outer shell even before the inner shell is filled to capacity.