The properties of atoms can be understood in terms of Quantum Theory, which involves the Heisenberg Uncertainty Principle and the Schrödinger Wave Equation.

Quantum Theory: A theory that states that the energy of an object can only change by discrete steps. A change involves a packet of energy called a quantum.

Heisenberg Uncertainty Principle: The position and momentum of a particle cannot both be known simultaneously. This implies that in an atom the position and momentum of an electron cannot both be known simultaneously. (Thus a model of an atom containing electrons in fixed orbits around the nucleus is untenable.)

Schrödinger Wave Equation: A mathematical expression ascribing wave-like properties to matter. When applied to atoms it describes the properties of electrons in atoms. This equation gives rise to the concepts of energy levels, atomic orbitals and quantum numbers.

Electronic energy levels: Allowed energies of electrons in atoms.

Atomic orbital: A mathematical expression from the Schrödinger Wave Equation from which, for each energy level, the probability of finding the electron at different positions from the nucleus can be calculated. The atomic orbital can be depicted as an "electron-cloud" with the nucleus at the centre, the denser the cloud the greater the probability of the electron being there. Only two electrons can occupy the same orbital.

Quantum numbers: Numbers which label the orbital and spin of an electron.

Electron pair: Two electrons in the same orbital. They must have opposite spins.

Spin of an electron: The intrinsic angular momentum of an electron. Occurs in only two senses denoted and .

Electron shells: The electrons in an atom exist in shells, each shell being made up of atomic orbitals or subshells.

Principal quantum number: Symbol n, an integer, 1,2 3... which defines the shell. The smaller n is, the lower the energy of the electron (more energy required to remove the electron from the atom), and the closer on average it is to the nucleus. First character in designation of an orbital.

Azimuthal quantum number: Symbol l, defines the subshell or kind of orbital, and can have the values 0,1,...,n–1. An orbital with l = 0 is called an s orbital; with l = 1 is called a p orbital with l = 2 is called a d orbital; with l = 3 is called an f orbital. Second character in designation of an orbital.

Magnetic quantum number: Symbol m_l, specifies the particular orbital of a subshell and can have values -l, -l+1, ..., 0, ..., l–1, l.

Spin quantum number: Symbol m_s, specifies the spin of an electron and can have values of +½ () or –½ ().

Occupancy of shells: The first shell, n = 1, can hold 2 electrons in one orbital, labelled 1s. (l = 0 for an s orbital)
The second shell, n = 2, can hold 8 electrons in four orbitals,
one labelled 2s and three labelled 2p. (l = 1 for a p orbital).
The third shell can hold 18 electrons in nine orbitals, one 3s, three 3p and five 3d. (l = 2 for a d orbital)
The fourth shell, n = 4, can hold 32 electrons in 16 orbitals, one 4s, three 4p, five 4d and seven 4f. (l = 3 for an f orbital)
Within a shell the energy levels of the orbitals (subshells) is s < p < d < f.

The bottom line in many periodic table gives the number of electrons in the shells in the ground state of that element.

Ground state: The state of an atom when all the electrons are in the lowest allowed energy levels.

Electron configuration: A statement of the arrangement of electrons in the orbitals.
Example: Cl, 1s² 2s²p⁶ 3s²p⁵.
Each principal quantum number is shown only once and the number of electrons in each subshell is shown as a superscript following the symbol for the orbital.

The ground state electron configuration of any element can be written down by filling the orbitals in order using the energy levels:

1s < 2>s < 2p < 3s <3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f

Valence electrons: Those electrons in the outermost shell and in unfilled subshells.
Valence electrons are involved in chemical bonds - section 4.

The Periodic Table: A table showing the elements in rows and columns in a manner which shows up relationships between the properties of the elements.

Periods: Rows of the periodic table. Elements in the same row are in the same period.
Example: calcium, Ca, and copper, Cu, are both in the 4th period The number of the period (row) is equal to the principal quantum number of the outermost valence shell of the atoms.

Groups: Columns of the periodic table. Elements in the same column are in the same group and have the same number of valence electrons (which accounts for their similarities).
Example: carbon, C, and tin, Sn, are both in group 14 and both have four valence electrons. This numbering replaces a previous system, shown as Roman numbers on the table, still used by some older chemists.

Blocks: Groups having the same valence orbitals.
Groups 1-2 are s-block because their elements have only s valence electrons;
Groups 3-12 are d-block because their elements have only s and d valence electrons;
Groups 13-18 are p-block because their elements have s and p valence electrons.

Alkali metals: The metals (elements) of Group 1.

Alkaline earth metals: The metals (elements) of Group 2.

Halogens: Elements of Group 17.

Halide: A binary compound of a halogen and another element.
Examples: HCl, CaCl₂, PCl₃,
or with a group
Example: CH₃Cl, chloromethane but also called methyl chloride; see section 6-2.

Halide ion: Monoatomic anion of a halogen.
Example: chloride ion, Cl¯

Transition metals: The metals (elements) of the d-block.

Ionisation energy:
The first ionisation energy is the minimum energy required to remove an electron from a neutral atom in the gas phase:

The second ionisation energy is the minimum energy to remove an electron from this gaseous ion:

Similarly for successive ionisation energies (I.E.). The variation of I.E with position in the periodic table is important in understanding the chemical properties of the elements. In general the ionisation energy increases from left to right in a period as the number of protons in the nucleus is increasing and therefore the attractive force between it and the electron is increasing. The first I.E. of the first element of a period is much lower than that of the last element in the previous period as the electron lost is from a shell of higher principal quantum number and hence energy.

Excited state: The state of an atom when an electron is in an orbital of energy greater than that in the ground state. When an electron changes energy level (orbital) a quantum of energy is emitted or absorbed as a photon.

Photon: A particle-like package of electromagnetic radiation. The energy, E, of the photon is related to the frequency, ν, of the radiation by the expression E = hν where h is the Planck constant.

EXERCISES

Write the electron configuration of the ground states of the following elements:

1. selenium
2. carbon
3. fluorine
4. iron
5. arsenic
6. silver

answers 2 to 6

7-12. Give a possible value for the principal quantum number and for the azimuthal quantum number
for a valence electron of these elements
7. selenium
8. carbon
9. fluorine
10. iron
11. arsenic
12. silver

Example: 7. selenium, Se
Answer: For Se the valence electrons are 4s and 4p.
For 4 s: n = 4, l = 0
For 4p: n = 4, l = 1

answers 8 to 12

Give the orbital of an electron with each of the following quantum numbers:
13. n = 3, l = 2
14. n = 2, l = 1
15. n = 5, l =0
16. n = 6, l =3

13. Example: n = 3, l = 2
Answer: 3d

In which period, group and block of the periodic table are the following elements?

17. Example: Strontium

Answer: group 2, 5th period, s-block

18. xenon
19. gold
20. silicon
21. lithium

22. The second ionisation energy of sodium is much greater than that of magnesium.
Explain in terms of their electron configurations.
(Hint: write down the electron configurations and see which electrons are being lost.)
answers 14+