The Quantum Mechanical Model of the Atom

Bohr model establishes the concept of definite electron energy levels within atoms. But Bohr's model was rather simplistic and as scientists made more discoveries about more complex atoms, Bohr's model was modified and eventually was replaced by more sophisticated models.

The Quantum Mechanical Model of the atom presents a more accurate model of the atom. It is a more sophisticated model based on complex mathematical calculations and interpretations. We will take a look at this model and summarize the results based on these mathematical calculations without carrying them out ourselves.

The Quantum Mechanical Model introduces the concept of:

The following table summarizes the number of orbitals in each sublevel.

Type of Atomic Orbital Number of orbitals
There is 1 s -type orbital.
There are 3 p -type orbitals.
There are 5 d -type orbitals.
There are 7 f-type orbitals.*

3E - Electrons in the Sublevels

Each orbital can contain a maximum of two electrons. Wolfgang Pauli states that if two electrons occupy the same orbital they must have opposite spin. This is known as the Pauli exclusion principle.

Recall, that from the Bohr model ( the maximum number of electrons that can occupy a principal energy level n is

A detail look at principal energy level 3, n = 3

  1. Bohr model predicts that a maximum of 2(3)2 = 18 electrons can reside in the 3rd principal energy level.
  2. Quantum Mechanical Model of the atom predicts that in principal energy level 3, there are 3s, 3p, and 3d.
  3. In any s-subshell, there is 1 atomic orbital. Therefore, there is 1 atomic orbital in the 3s sublevel.
  4. In any p-subshell, there are 3 atomic orbitals. Therefore, there are 3 atomic orbitals in the 3p sublevel.
  5. In any d-subshell, there are and 5 atomic orbitals. Therefore, there are 5 atomic orbitals in the 3d sublevel.
  6. Since it follows that:
  7. Add up the number of electrons in step 6 to get a total of 2 + 6 + 10 = 18 electrons (as predicted in step 1). The Quantum Mechanical Model allows us to see how the 18 electrons are distributed in each sublevel within the 3rd principal energy level.

    Here is an example of orbital configuration for Hydrogen, Helium and Carbon.

        The simplest atom hydrogen has 1 electron.  It will go into the 1s orbital with a spin in either direction.  We can represent this with either an orbital filling diagram or an electron configuration.

        The next atom is helium.  It has 2 electrons.  As a result according to the Pauli Exclusion Principle, no two electrons may have the same set of four quantum numbers.  Thus the two electrons occupying the 1s orbital must have different spins.  This can be seen on the orbital filling diagram, but not on the electron configuration which provides less information.

        The next important atom for instruction is C.  It has six electrons.  But how are those electrons arranged?

It turns out that the two electrons filling the 2p orbitals will separate into different orbitals with parallel spins.  This is the result of Hund's Rule.  The most stable arrangement of electrons in a sublevel is the one with the greatest number of parallel spins.  The result is that each orbital will have one electon spinning in a common direction before two electrons will fill the same orbital.  Notice once again that the electron configuration does not make this distinction.

3.2 - Electron Configurations of Atoms

When electrons fill the energy levels, it fills principal energy levels, sublevels, atomic orbitals from lowest energy first. to view the order in which the sublevels are ordered according to energy. Look carefully and you will see:

  1. some 4 sublevel is lower in energy than a 3 sublevel (i.e. 4s is lower in energy than 3d;)
  2. some 5 or 6 sublevel is lower in energy than a 4 sublevel (i.e. 5p and 6s are lower in energy than 4f; )

At first glance it appears that the sequence for electrons to fill the atomic orbitals are of random order. Read on to find an easier way to remember the order of atomic orbitals according to energy.

3F - Filling Order of the Sublevels

How do we go about remembering the sequence in which electrons fill the sublevels?

The order in which electrons fill the sublevels is easy to remember if you follow these steps:
  1. Write the principal energy levels and their sublevels on separate lines (as shown on the diagram).
  2. Draw arrows over the sublevels (see the red diagonal lines on the diagram by placing your mouse over the diagram).
  3. Join the diagonal lines from end to end (click on the diagram to see how I have joined the red diagonal lines).
  1. Follow the arrows. The sublevels are magically arranged in the correct sequence from lowest energy. compare the order of filling sublevel sequence with the energy diagram of the sublevels.

3G - Electron Configuration Notations

There is a way to represent precisely the electron arrangement in atoms. Let's take a look at the simplest atom, hydrogen.

A hydrogen atom has 1 electron. That electron will occupy the lowest principal energy level, n = 1, and the only sublevel, s. We denote the electron configuration of hydrogen as


The table below shows the electron configuration for the first 20 elements on the periodic table.
NB: the superscripts add up to the atomic number of the atom.
Name Atomic Number Electron Configuration
Hydrogen 1 1s1
Helium 2 1s2
Lithium 3 1s2 2s1
Beryllium 4 1s2 2s2
Boron 5 1s2 2s22p1
Carbon 6 1s2 2s22p2
Nitrogen 7 1s2 2s22p3
Oxygen 8 1s2 2s22p4
Fluorine 9 1s2 2s22p5
Neon 10 1s2 2s22p6
Sodium 11 1s2 2s22p63s1
Magnesium 12 1s2 2s22p63s2
Aluminum 13 1s2 2s22p63s23p1


1s2 2s22p63s23p2
Phosphorus 15 1s2 2s22p63s23p3
Sulfur 16 1s2 2s22p63s23p4
Chlorine 17 1s2 2s22p63s23p5
Argon 18 1s2 2s22p63s23p6
Potassium 19 1s2 2s22p63s23p64s1
Calcium 20 1s2 2s22p63s23p64s2

3H - Electron Configuration and the Periodic Table

There is a pattern between the electron configuration for the elements and their positions on the periodic table. You should take a look at and look closely at the first 20 elements. Compare the electron configuration of an element and its position on the periodic table.