Energy Levels, Sublevels & Orbitals (HL IB Chemistry)

What are electron shells?

• The arrangement of electrons in an atom is called the electronic configuration
• Electrons are arranged around the nucleus in principal energy levels or principal quantum shells
• Principal quantum numbers (n) are used to number the energy levels or quantum shells
  • The lower the principal quantum number, the closer the shell is to the nucleus
  • The higher the principal quantum number, the greater the energy of the electron within that shell
• Each principal quantum number has a fixed number of electrons it can hold
  • n = 1 : up to 2 electrons
  • n = 2 : up to 8 electrons
  • n = 3 : up to 18 electrons
  • n = 4 : up to 32 electrons
• There is a pattern here - the mathematical relationship between the number of electrons and the principal energy level is 2n² 
  • So for example, in the third shell n = 3 and the number of electrons is 2 x (3²) = 18

 Principle quantum shells

Electrons are arranged in principal quantum shells, which are numbered by principal quantum numbers

What are subshells?

• The principal quantum shells are split into subshells which are given the letters s, p and d
  • Elements with more than 57 electrons also have an f subshell
  • The energy of the electrons in the subshells increases in the order s < p < d
• The order of subshells overlap for the higher principal quantum shells as seen in the diagram below:

Principle Quantum Number and Sub-Shells

Electrons are arranged in principal quantum shells, which are numbered by principal quantum numbers

What are orbitals?

• The subshells contain one or more atomic orbitals
• Orbitals exist at specific energy levels and electrons can only be found at these specific levels, not in between
  • Each atomic orbital can be occupied by a maximum of two electrons
• The orbitals have specific 3D shapes:

The shape of s and p orbitals

Representation of orbitals (the dot represents the nucleus of the atom) showing spherical s orbitals (a), p orbitals containing ‘lobes’ along the x, y and z axis

• Note that the shape of the d orbitals is not required for IB Chemistry

Summary of s and p orbitals

An overview of the shells, subshells and orbitals in an atom

Ground state

• The ground state is the most stable electronic configuration of an atom which has the lowest amount of energy
• This is achieved by filling the subshells of energy with the lowest energy first (1s)
  • This is called the Aufbau Principle
• The order of the subshells in terms of increasing energy does not follow a regular pattern at n = 3 and higher

The Aufbau Principle

The Aufbau Principle - following the arrows gives you the filling order

• The principal quantum shells increase in energy with increasing principal quantum number
  • E.g. n = 4 is higher in energy than n = 2
• The subshells increase in energy as follows: s ＜ p ＜ d ＜ f
  • The only exception to these rules is the 3d orbital which has slightly higher energy than the 4s orbital, so the 4s orbital is filled before the 3d orbital

Energy Levels

Relative energies of the shells and subshells

• Each shell can be divided further into subshells, labelled s, p, d and f
• Each subshell can hold a specific number of orbitals:
  • s subshell : 1 orbital
  • p subshell : 3 orbitals labelled p_x, p_y and p_z
  • d subshell : 5 orbitals
  • f subshell : 7 orbitals
• Each orbital can hold a maximum number of 2 electrons so the maximum number of electrons in each subshell is as follows:
  • s : 1 x 2 = total of 2 electrons
  • p : 3 x 2 = total of 6 electrons
  • d : 5 x 2 = total of 10 electrons
  • f : 7 x 2 = total of 14 electrons
• In the ground state, orbitals in the same subshell have the same energy and are said to be degenerate, so the energy of a px orbital is the same as a p_y orbital

Division of Shells Diagram

Shells are divided into subshells which are further divided into orbitals

Summary of the Arrangement of Electrons in Atoms Table

What is the shape of an s orbital?

• The s orbitals are spherical in shape
• The size of the s orbitals increases with increasing shell number
  • E.g. the s orbital of the third quantum shell (n = 3) is bigger than the s orbital of the first quantum shell (n = 1)

s orbital diagram

The s orbitals become larger with increasing principal quantum number

What is the shape of a p orbital?

• The p orbitals are dumbbell-shaped
• Every shell has three p orbitals except for the first one (n = 1)
• The p orbitals occupy the x, y and z axes and point at right angles to each other, so are oriented perpendicular to one another
• The lobes of the p orbitals become larger and longer with increasing shell number

p orbital diagram

The p orbitals become larger and longer with increasing principal quantum number