II. Orbital and Periodicity

Key focus of this chapter: periodic table with groups

This chapter focuses on periodic table with groups and gives concise summaries of the important things about orbital theory, shapes of orbitals, rules of filling up electrons in orbitals, quantum numbers, electron configuration, atomic radius, ionization, and electron affinitive in more detail.

A. Orbital theory

1. Bohr’s atomic model

Model for hydrogen atom.
The paths of electrons, which are circling around a nucleus, are called electron shells.
Each electron shell (number of electron shell =n) has an energy difference level → the farther from the nucleus, the greater the difference of energy level → K(n=1) < L(n=2) < M(n=3) < N(n=4)

Fig. 1 Bohr’s atomic model

• Energy change when electrons move to other electron shells

Classification	Features
Ground state electrons	• Normal and stable state of electrons with low energy • When ground state electrons at a lower shell go to the higher shell, energy is absorbed. K (n=1) → L (n=2)
Excited state electrons	• Abnormal and unstable state of electrons with the high energy • When excited state electrons at a higher shell go to the lower shell, energy is emitted. L (n=2) → K (n=1)

Fig2. Ground and excited state electrons

2. Lyman, Balmer, and Paschen series

Classification	Features
Lyman series	• When excited state electrons at a high shell go down to K (n=1) shell, energy is emitted. • Ultraviolet region
Balmer series	• When excited state electrons at a high shell go down to L (n=2) shell, energy is emitted. • Visible region
Paschen series	• When excited state electrons at a high shell go down to M (n=3) shell, energy is emitted. • Infrared region

3. Modern atomic model

: limited theory of Bohr’s atomic model → modern atomic model (orbital theory)

a. Orbital theory

Electrons travel around nucleus, but not in a fixed path → high probability of finding an electron in a certain position → orbital
Each electron shell is composed of several orbitals (s, p, d, f)

b. Electron shells and orbitals

With the increasing number of electron shells (n), the number of orbitals (s, p, d, f) at each electron shell is increased.

Electron shells	Orbitals
n= 1	1s
n=2	2s 2p
n=3	3s 3p 3d

Fig. 3 Modern atomic model

B. Shapes of orbitals

Classification	Features
s orbitals	• Spherical shape • Closest orbital to nucleus • Spatial orientation of the orbital = zero → S orbital electrons are spread near nucleus with no direction • Magnetic quantum number, ml =0 • Orbital holds 2 electrons → 1×2 = 2 electrons in s orbitals
p orbitals	• Dumbbell shape • 3 orientations of X, Y, or Z coordinate axes → Px, Py, or Pz • Magnetic quantum number, ml = -1, 0, +1 • Each orbital holds 2 electrons → 3×2 = 6 electrons in p orbitals
d orbitals	• Usually have a cloverleaf shape • 5 different orbital shapes → dxy, dxz, dyz, dx2- y2, dz2 • Each orbital holds 2 electrons → 5×2 = 10 electrons in d orbitals • Transitional metals region in periodic table
f orbitals	• Complex shape with eight lobes • 7 different orbital shapes • Each orbital holds 2 electrons → 7×2 = 14 electrons in f orbitals

C. Rules of filling up electrons in orbitals

: electrons are expressed by arrow (↓,↑) in the orbital filling diagram.

Classification	Features
Pauli exclusion principle
Hund’s rule
Filling order of different orbitals

D. Quantum numbers

: expressing three variable wave functions (n, l, m_l) by electrons in a space.

Classification	Features
The principal quantum number (n), shell
Angular-momentum quantum number, subshell (l)
Magnetic quantum number (Ml)

• Combined quantum numbers (n, l, m_l)

Principal quantum number n	Angular momentum quantum number l	Orbital notation	Magnetic quantum number ml	Number of orbital(s) in subshell	Maximum electrons in shell (2n2)
1	0	1s	0	1
2	0 1	2s 2p	0 -1, 0, +1	1 3
3	0 1 2	3s 3p 3d	0 -1, 0, +1 -2, -1, 0, +1, +2	1 3 5
4	0 1 2 3	4s 4p 4d 4f		1 3 5 7

E. Electron configuration

1. Filling order of electrons in orbitals (from low to high energy)

1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → ….

Fig. 4 Position of orbitals in the periodic table

2. Electron configuration

: expressing of energy level for every element by occupied electrons in orbitals.

	Ground state electron configuration	Shorthand electron configuration	Orbital filling diagrams
Be
Ar
V

Fig. 5 Ground state electron configuration in the periodic table

** Exceptional atoms of electron configuration

Cr, Cu, Nb, Mo, Ru, Rh, Ag (dark red color above)

Ex/ Cr: 1s²2s²2p⁶3s²3p⁶4s²3d⁴ (X) → 1s²2s²2p⁶3s²3p⁶4s¹3d⁵ (O)

Cu: 1s²2s²2p⁶3s²3p⁶4s²3d⁹ (X) → 1s²2s²2p⁶3s²3p⁶4s¹3d¹⁰ (O)

F. Application of electron configuration

1. Counting of unpaired electrons: half filling electrons in orbital

2. Ground state and excited state

Ground state: normal state of electron(s)

Excited state: moving electron(s) from low level of orbital to high level of orbital

G. Electromagnetic spectrum

1. Light

Classified by wavelength (λ)
The speed of light (C), C=3.00 × 10⁸ m/s (all lights have same speed)
Frequency (ν): number of wave peaks per second (hertz, Hz, s^-1)

** Photoelectric effect: ejected electrons from metal surfaces by irradiation

2. Energy (E)

Long wavelength → low frequency → low energy
Short wavelength → high frequency → high energy
Ex/ Gamma rays → short wavelength → high energy

3. Order of energy

H. Periodicity

1. Periods

Seven rows (n = 1, 2, 3, 4, 5, 6, 7)
Indicating number of shell

2. Groups

18 columns (1A – 8A, 1B –8B)
Indicating similar chemical characteristics within the same group (atoms in the same group have the same outermost electrons)

Ex/ Be, Mg, and Ca (group 2A) have similar chemical characteristics (they have 2 outermost electrons).

Fig. 6 Periods and groups

a. Metal and nonmetal

Classification	Characteristics
Metal	• Tendency to move out electrons from atoms → tendency to become cation by losing electrons (reducing agents) → good conductivity for heat and electricity • Malleability • Ductility • Shiny luster • Typically solids
Nonmetal	• Tendency to move electrons into atoms → tendency to becoming anions by gaining electrons (oxidizing agents) → poor conductivity for heat and electricity • Brittleness

b. Classification of groups

Fig. 7 Classification of groups in periodic table

Classification	Sub classification	Features
Metal groups	Alkali metals	• Group 1A except H (Li, Na, K, Rb, Cs, Fr) • One electron at their outermost shell → tending to lose one electron to become (+1) cation (good conductors) → the strongest reducing agent groups → highly basic • The lowest M.P, B.P, and density group • Found as salt forms
	Alkaline earth metals	• Group 2A (Be, Mg, Ca, Sr, Ba, Ra) • Two electrons in their outermost shell → tending to lose two electrons to become (+2)cations → the second strongest reducing agents → basic • The second lowest M.P, B.P, and density group • Found as salt forms
	Transition metals
Semi metals (metalloid)		• Intermediate characteristics between metals and nonmetals • B, Si, Ge, As, Sb, Te, At
Nonmetals	Halogen group	• Group 7A (F, Cl, Br, I, At) • Seven electrons in the outermost shell → tending to gain one electron to become (–1)anion → strong oxidizing agent → acidic • Corrosive and colorful nonmetals • Found in binary compound
Nonmetals	Noble gas group	• Group 8A (He, Ne, Ar, Kr, Xe, Rn) • Very low reactivity because of 8 electrons (except He) in their outermost shells • Colorless and odorless

I. Atomic radius

: distance from a nucleus to outermost electrons.

1. Atomic radius in periodic table

In the same period, when the atomic number is increased, the atomic radius is decreased because the attraction force between the protons (+) and outer electrons (-) is increased.

Li > Be > B > C > N > O > F

In the same group, when the atomic number is increased, the atomic radius is increased because the electron shells are increased.

Li < Na < K < Rb < Cs < Fr

In the isoelectronic, cationic (metallic) radius is smaller than its neutral atom and anionic (non-metallic) radius is greater than its neutral atom.

Ca²⁺ < K⁺ < Ar < Cl^– < S^2-

2. Cationic (metallic) and anionic (nonmetallic) radius

Classification	Features
Cationic(metallic) atoms
Anionic(nonmetallic) atoms

J. Ionization energy (E_i)

: positive energy to get rid of an outermost electron of an atom.

Atom + energy → Cationic atom + e^–

Fig. 8 Ionization energy of Li

Ei 1, (first ionization energy): positive energy to get rid of the first outermost electron in an atom → (high energy with stable outermost electrons, such asoctet rule)

Ar > Be > Li

Ei 2, (second ionization energy): positive energy to get rid of the second outermost electron in an atom → (high energy with 1 outmost electron)

Li > Ar > Be

	Ground state electron configuration	Outermost electron(s)	Ei 1 (kJ/mol)	Ei 2 (kJ/mol)	Ei 3 (kJ/mol)
Li		1	520	7,300	11,820
Be		2	900	1,760	14,850
Ar		8	1,520	2,670	3,930

a. General trend

In the same period, with the increasing atomic number, the E_i is increased.

O < F < Ne

In the same group, with the increasing atomic number, the E_i is decreased.

He > Ne > Ar

The half-filled or fully-filled electrons in each orbital have a strong E_ito remove an outermost electron.

Therefore, ionization energy: Be > B

Therefore, ionization energy: N > O > C

Fig. 9 Ionization energy of the atoms

K. Electron affinitive (E_ea)

: negative (emitting) energy when atom accepts an electron and becomes an anionic atom.

Atom + e^– → anionic atom + energy

Fig. 10 Electron affinitive of F

a. General trends

The E_eaof 8A group (noble gases) is zero.
In the same period, with the increasing atomic number, the E_ea is increased.

N < O < F

In the same group, with the increasing atomic number, the E_ea is decreased.

Cl > Br > I ** exception (F < Cl)

An atom that is 2/3 half-filled in orbitals has the stronger E_ea than 3/3 half-filled in orbitals.

Therefore, electron affinitive: C > N

An atom that is 2/3 fully-filled in orbitals, has the stronger E_ea than 3/3 fully-filled in orbitals.

Therefore, electron affinitive: F > Ne

Fig. 11 Electron affinitive of the atoms

L. Tendency of atoms in periodic table

In the direction left and downward, metallic properties, atomic radius, and intermolecular forces are increased.
In the direction right and upward, electronegativity, ionization energy, and electro affinity are increased.

	Increasing	Decreasing
Going left and down (from periodic table)	• Metallic character • Atomic radius • Intermolecular forces (London dispersion)	• Electronegativity • Ionization energy • Electro affinity

Fig 12. Tendency of atoms in periodic table