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:
subshells or sublevels(s, p,d,f)
and 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 ftype
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
 Bohr model predicts that a maximum of 2(3)^{2} = 18 electrons
can reside in the 3rd principal energy level.
 Quantum Mechanical Model of the atom predicts that in principal energy
level 3, there are 3s, 3p, and 3d.
 In any ssubshell, there is 1 atomic orbital. Therefore,
there is 1 atomic orbital in the 3s sublevel.
 In any psubshell, there are 3 atomic orbitals. Therefore,
there are 3 atomic orbitals in the 3p sublevel.
 In any dsubshell, there are and 5 atomic orbitals.
Therefore, there are 5 atomic orbitals in the 3d sublevel.
 Since
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
 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:
 some 4 sublevel is lower in energy than a 3 sublevel (i.e. 4s is
lower in energy than 3d;)
 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: 
 Write the principal energy levels and their sublevels on separate lines (as shown on the diagram).
 Draw arrows over the sublevels (see the red diagonal lines on the diagram by placing your mouse over the diagram).
 Join the diagonal lines from end to end (click on the diagram to see how I have joined the red diagonal lines).

 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
Similarly,
 Helium has 2 electrons; the 2 electrons
both occupy the s sublevel in principal energy level 1.
 Helium's electron configuration is 1s^{2}
 Lithium has 3 electrons; 2 of the 3 electrons
occupy the s sublevel in principal energy level 1. The 3rd electron
must go in the next available sublevel, 2s.
 Lithium's electron configuration is 1s^{2}
2s^{1}
 Beryllium has 4 electrons; 2 of the 3 electrons
occupy the s sublevel in principal energy level 1. The 3rd and 4th
electrons must go in the next available sublevel, 2s.
 Beryllium's electron configuration is 1s^{2}
2s^{2}
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 
PERIOD
1 
Hydrogen 
1 
1s^{1} 
Helium 
2 
1s^{2} 
PERIOD
2 
Lithium 
3 
1s^{2}
2s^{1} 
Beryllium 
4 
1s^{2}
2s^{2} 
Boron 
5 
1s^{2}
2s^{2}2p^{1} 
Carbon 
6 
1s^{2}
2s^{2}2p^{2} 
Nitrogen 
7 
1s^{2}
2s^{2}2p^{3} 
Oxygen 
8 
1s^{2}
2s^{2}2p^{4} 
Fluorine 
9 
1s^{2}
2s^{2}2p^{5} 
Neon 
10 
1s^{2}
2s^{2}2p^{6} 
PERIOD
3 
Sodium 
11 
1s^{2}
2s^{2}2p^{6}3s^{1} 
Magnesium 
12 
1s^{2}
2s^{2}2p^{6}3s^{2} 
Aluminum 
13 
1s^{2}
2s^{2}2p^{6}3s^{2}3p^{1} 
Silicon 
14

1s^{2}
2s^{2}2p^{6}3s^{2}3p^{2} 
Phosphorus 
15 
1s^{2}
2s^{2}2p^{6}3s^{2}3p^{3} 
Sulfur 
16 
1s^{2}
2s^{2}2p^{6}3s^{2}3p^{4} 
Chlorine 
17 
1s^{2}
2s^{2}2p^{6}3s^{2}3p^{5} 
Argon 
18 
1s^{2}
2s^{2}2p^{6}3s^{2}3p^{6} 
PERIOD
4 
Potassium 
19 
1s^{2}
2s^{2}2p^{6}3s^{2}3p^{6}4s^{1} 
Calcium 
20 
1s^{2}
2s^{2}2p^{6}3s^{2}3p^{6}4s^{2} 
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.
 Elements belonging in Group IA (eg  H, Li,
Na, K) all have electron configuration ending in ns^{1
}
(the superscript of '1' indicates there is 1 valance electron for elements belonging to Group IA).
 Elements belonging in Group IIA (eg  Be,
Mg, Ca) all have electron configuration ending in ns^{2
}(the superscript of '2' indicates there are 2
valence electrons for elements belonging to Group IIA).
 Elements belonging in Group IIIA (eg  B,
Al) all have electron configuration ending in ns^{2}np^{1
}
(the superscripts total to '3' indicates there are 3
valence electrons for elements belonging to Group IIIA).
 Elements belonging in Group IVA (eg  C, Si)
all have electron configuration ending in ns^{2}np^{2
}
(the superscripts total to '4' indicates there are 4
valence electrons for elements belonging to Group IVA).
 Elements belonging in Group VA (eg  N, P)
all have electron configuration ending in ns^{2}np^{3
}
(the superscripts total to '5' indicates there are 5
valence electrons for elements belonging to Group VA).
 Elements belonging in Group VIA (eg  O, S)
all have electron configuration ending in ns^{2}np^{4
}
(the superscripts total to '6' indicates there are 6
valence electrons for elements belonging to Group VIA).
 Elements belonging in Group VIIA (eg  F,
Cl) all have electron configuration ending in ns^{2}np^{5
}
(the superscripts total to '7' indicates there are 7
valence electrons for elements belonging to Group VIIA).
 Elements belonging in Group VIIIA (eg  He,
Ne, Ar) all have electron configuration ending in ns^{2}np^{6
}
(the superscripts total to '8' indicates there are 8
valence electrons for elements belonging to Group VIIIA).
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