Quantum mechanical model of the atom

The 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

• sublevels (s, p, d, f)
• atomic orbitals

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

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

* (University of Kentucky)

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.

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 3 sublevels: 3s, 3p, and 3d.
3. In any s sublevel, there is 1 atomic orbital. Therefore, there is 1 atomic orbital in the 3s sublevel.
4. In any p sublevel, there are 3 atomic orbitals. Therefore, there are 3 atomic orbitals in the 3p sublevel.
5. In any d sublevel, there are and 5 atomic orbitals. Therefore, there are 5 atomic orbitals in the 3d sublevel.
6. Since each atomic orbital can accommodate 2 electrons, it follows that:
   • 1 atomic orbital in 3s sublevel x 2 electrons/orbital = 2 electrons can reside in the 3s sublevel
   • 3 atomic orbitals in 3p sublevel x 2 electrons/orbital = 6 electrons can reside in the 3p sublevel
   • 5 atomic orbitals in 5d sublevel x 2 electrons/orbital = 10 electrons can reside in the 3d sublevel
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.

Distribution of electrons

Principal energy level, n	Number of sublevels	Type of atomic orbital	Number of atomic orbitals	Maximum number of electrons per sublevel	Maximum total number of electrons
1	1	1s	1	1 orbital x 2 electrons/orbital = 2	2*
2	2	2s 2p	1 3	1 orbital x 2 electrons/orbital = 2 3 orbitals x 2 electrons/orbital = 6	2 + 6 = 8*
3	3	3s 3p 3d	1 3 5	1 orbital x 2 electrons/orbital = 2 3 orbitals x 2 electrons/orbital = 6 5 orbitals x 2 electrons/orbital = 10	2 + 6 + 10 = 18*
4	4	4s 4p 4d 4f	1 3 5 7	1 orbital x 2 electrons/orbital = 2 3 orbitals x 2 electrons/orbital = 6 5 orbitals x 2 electrons/orbital = 10 7 orbitals x 2 electrons/orbital = 14	2 + 6 + 10 + 14 = 32*

* Numbers on the last column is equivalent to the prediction using the formula 2n².

Content suitability

BCIT courses: CHEM 0011