Periodicity Of Elements

The essential model or theory to understand an elements chemical properties came from the early birth of quantum mechanics and is known as electron configuration. The element is modeled as an atom with its "number", the atomic number ( Z ) which represents the number of protons, and therefore the number of electrons as well( in ground state ). The periodicity of the elements might be explained by the electron structure of the atom which can in turn be explained by quantum theory.

An electron within the atom can be described by the four quantum numbers:

• n    = the principal quantum number( or simply, quantum number ), e.g: 1,2,3…
• l     = the orbital quantum number( or simply, angular number ), e.g: 0,1,2…
• m _l = the orbital magnetic quantum number( or simply, magnetic number ), e.g: -2,-1,0,+1,+2…
• m _s = the spin magnetic quantum number( or simply, spin number ), e.g: ⁺½ or ⁻½.

The four quantum numbers designate specific levels, orbitals, magnetics, and spins of electrons . This explains that they are describing the detailed characteristic of the electrons in the atom. The principal quantum number n describes the energy level of the electron shell. When value of n is higher, the number of principal electron shell is greater, which means a greater distance between the farthest electron and the atoms nucleus. As a result the size and radius of the atom increases. The angular quantum number l describes the shape of the orbital. Each quantum number is composed of one or more subshells( orbital ). The detail of possible subshells are shown in following table:

Orbital label	l	Max electrons	Spectroscopic Name
s	0	2	Sharp
p	1	6	Principal
d	2	10	Diffuse
f	3	14	Fundamental
g	4	18	( simply in alphabet after f )
h	5	22
i	6	26

The magnetic quantum number describes the number of orbitals and its orientation in the space of a specific orbital. Consequently, its value depends on the orbital angular momentum quantum number l. The possible value of m _l is an interval ranging from -l to +l, so it may be zero, a negative integer, or a positive integer. Unlike n, l, and m _l , the spin magnetic quantum number does not depend on another quantum number. It defines the direction of the electrons spin , which value may have ⁺½ (represented by ↾ "spin up") or ⁻½(represented by ⇃ "spin down.")
So far we have explanations for the four quantum numbers that model an elemental atom.

Principles

There are principles that must be followed when writing electron configuration; these principles are described below:

• Pauli Exclusion Principle or Quantum State

  This principle states that:

  There are no two electrons in an atom can exist in the same quantum state .

  Because the state of any electron is specified by the quantum numbers n, l, m _l and m _s , the principle simply states that no two electron can have the same set of the four quantum numbers .

• Aufbauf Principle or Constructing Up Principle

  states that:

  A maximum of two electrons ...

• Hund's Rule or Pairing Rule

  states the following:

  Pairing of electrons take place when all the available degenerate orbitals in a given subshell are filled with one electron each.

  Orbitals may have identical energy levels when they are of the same subshell (l = 1, then m _l are -1, 0, 1, which have similar energy). Then when assigning electrons in orbitals, each electron will first fill all the orbitals with similar energy (read: degenerate orbitals) before pairing with another electron.

Noble Gas Notation

Noble Gas Notation takes a slightly different form as seen here:

[closest noble gas element] [ quantum number ][ orbital name ] ^{[ number of electrons ]}

Here are some samples (Noble Gasses are located in column 18 (IUPAC),) described below:

Element	Symbol	Atomic Number( Z )	Electron Configuration	Noble Gas Notation
Helium	He	2	1s²	1s²
Neon	Ne	10	1s² 2s² 2p⁶	[He] 2s² 2p⁶
Argon	Ar	18	1s² 2s² 2p⁶ 3s² 3p⁶	[Ne] 3s² 3p⁶
Krypton	Kr	36	1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶	[Ar] 3d¹⁰ 4s² 4p⁶
Xenon	Xe	54	1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 5s² 5p⁶	[Kr] 4d¹⁰ 5s² 5p⁶
…
and so on…

Writing Electron Configuration

Electron configuration follows this form:

[ quantum number ][ orbital name ] ^{[ number of electrons ]}

When writing the electron configuration, we must first write the energy level ( quantum number ) then the subshell (orbital number) and the superscript , which is the number of electrons in that specific subshell. Using these rules , we can now start writing the electron configuration for all the elements in the periodic table.

Consider the following element, Oxygen(O) with Z = 8:

Element:	Oxygen
Symbol:	O
Z:	8
Orbital Diagram:	⇅  ⇅   ⇅↾↾
Orbital Model:	2      2      2    1    1
Electron Configuration:	1s²    2s²      2p⁴
Noble Gas Notation:	[He] 2s² 2p⁴

CheckiO Quantum Task

Your task is to determine the atomic number and electron configuration in the noble gas notation as well as its orbital model , which is 0 - if there are no electrons, 1 - if the electron is in a degenerate orbital, and 2 - for electrons in a full orbital, by its symbolic element. The number of elements is limited to 118 (as of September First, 2013). This task will use superscript for the electron notation, as seen below:

Unicode superscript characters

Unicode	0	1	2	3	4	5	6	7	8	9
U+00Bx			x²	x³						x¹
U+207x	x⁰				x⁴	x⁵	x⁶	x⁷	x⁸	x⁹

assert( checkio( 'H' ) == [ "1", u"1s¹", "1" ] ), "First Test - 1s¹"
assert( checkio( 'He' ) == [ "2", u"1s²", "2" ] ), "Second Test - 1s²"
assert( checkio( 'Al' ) == [ "13", u"[Ne] 3s² 3p¹", "2 2 222 2 100" ] ), "Third Test - 1s² 2s² 2p6 3s² 3p¹"
assert( checkio( 'O' ) == ["8", u"[He] 2s² 2p⁴", "2 2 211"] ), "Fourth Test - 1s² 2s² 2p⁴"
assert( checkio( 'Li' ) == [ "3", u"[He] 2s¹", "2 1" ] ), "Fifth Test - 1s² 2s¹"

print('All done!')