TOPIC-3: ELECTRONS IN
ATOMS(Summer course)
Quantum Numbers and Electron Orbitals
In the wave mechanics the electrons in an atom
composed of more than one electron are distributed in
the shells. The shells are composed of one subshell or
many subshells,the subshells are made up of one
orbital or many orbitals. Each electron of an atom is
defined through three quantum numbers referring to
the shell, subshell and orbital.
Quantum Numbers and Electron Orbitals
• Principal Quantum number, n: The energy levels in atom are
divided into the shells represented by the principle quantum
number, “n”. As in the Bohr quantum theory, it may have
only positive, nonzero (n = 1, 2, 3, …..) integral values. In
addition to the numbers, to indicate the layers, some letters
are also used. The shells are the regions where electrons are
more likely to be found. The greater the n value, the farer
the shell from the nucleus.
• 1
2
3
4
5...
• K
L
M
N
O…
Quantum Numbers and Electron Orbitals
Angular momentum quantum number, l: Energy levels include
sub-energy levels. Consequently, shells are seperated into
subshells each of which is represented with angular
momentum quantum number “l” .This determines the
geometrical shape of the electron probability distribution. The
number “l” can have all values ranging from 0, 1, 2 to n-1. For
n=1 the maximum and unique value of “l” is 0 which means
that the level K contains one sub-level. For n=2 , “l” will have 0
and 1 values. Thus, L level is composed of two sub-levels. The
total number of sub-levels in a level is equal to the principal
quantum number. The sub-shells are indicated as below:
0
1
2
3
4
5
6…
s
p
d
f
g
h
i …
Quantum Numbers and Electron Orbitals
• To indicate a sub-shell in a shell, the principal quantum
number “n” and the angular momentum quantum number
are written next to each other . For the second shell (L), the
subshells s and p are indicated as 2s (n = 2, l = 0) and 2p (n =
2, l =1 ) .
• Magnetic quantum number, ml: Each subshell is composed
of one or more orbitals and each orbit in a sub-shell is
defined as magnetic quantum number “ml”. This number
may be a positive or negative integer including zero and
ranging from – l to +l.
Magnetic
quantum
number
ml
The
number
of
orbitals
in the
subshell
Principal
quantum
number
n
Orbital
quantum
number
l
Sub-shell
3
0
3s
0
1
1
3p
-1,0,1
3
2
3d
-2,-1,0,1,2
5
Quantum numbers and Electron
Orbitals
The shells and sub-shells of Hydrogen atom
s orbitals
s orbital: Spherically symmetric
p orbitals
p orbital: Electron density
is
in
form
of
a
dumbbell.Two lobes are
seperated by
a nodal
plane in which charge
density drops to zero.
d orbital
d orbital: There are 5 different type of d
orbitals.
Their
orientations
vary
respectively.
Electron Spin-The fourth Quantum Number
Stern-Gerlach experiment
Ag atoms vaporized in the oven are
collimated into a beam by the slit
and the beam is passed through a
non-uniform magnetic field. The
beam splits in two with two
opposite directions ( A spinning
unpaired electron behaves as two
magnets with opposite
pole
directions.
Electron Spin
Spin magnetic quantum
number, ms: An electron
generates a magnetic field
because of its spin on its axis.
As a result of this action (
spin at one direction, and at
the opposite direction) the
spin
magnetic
quantum
number may have values :
ms=+1/2 ve ms=-1/2.
Multielectron Atoms
Eş enerjili orbitaller
• Schrödinger developed his wave equation for the
hydrogen atom. For multielectron atoms a new factor
arises: mutual repulsions between electrons. Because
exact electron positions are not known,electron
repulsions can only be approximated.
Multielectron Atoms
• In multielectron atoms the attractive force of nucleus for a
given electron increases as the nuclear charge rises, which
leads to a decrease of the energy level of an orbital. Hence,
multielectron atoms have different orbital energies
The orbitals with different energy levels
Electron Configurations
The electron configuration of an atom is a designation of
how electrons are distributed among various orbitals.
Rules for Assigning Electrons in Orbitals
1. Electrons occupy orbitals in a way that minimizes the
energy of the atom.
Electron Configurations
• The diagram shows the order in which electrons
occupy orbitals in these shells, first 1s then 2s and
2p and so on. The order of the filling of orbitals has
been established by experiment, principally
through spectroscopy and it is the order that we
must follow in assigning electron configurations to
the element. Except for a few elements the order in
which the orbitals fill in:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p,
7s, 5f, 6d, 7p
Electron Configuration
2. No two electrons in an atom may have all four
quantum numbers alike (Pauli exclusion principle).
3. When orbitals of identical energy are available,
electrons initially occupy these orbitals singly. As a
result of this rule, known as Hund’s rule an atom
tends to have as many unpaired electrons as
possible. The electrons do this by seeking out empty
orbitals of similar energy in preference to pairing up
with other electrons in half-filled orbitals.
Notation of Electron Configuration
Since the atomic number of Carbon element is 6, in all of three
indications there are 6 electrons. The electrons are those with
parallel spins which occupy different orbitals in the same sub-shell
singly.
spdf notation (condensed)
spdf notation (expanded)
orbital diagram
The Aufbau Process
Aufbau means “constructing or building” and
what we do is assign electron configurations to
the elements in order of increasing atomic
number.
The Electron Configuration of some
elements(C, N, Ne, Na)
Valence Electrons
• Electrons that are added to the electronic shell of highest
principal quantum number(the outermost or valence shell)
are called valence electrons. The electron configuration of
Na is written below with the neon core ( 1s2s2p6 ) and for
the other third period elements only the valence-shell
electron configuration is shown.
• Na Mg Al
Si
P
S
Cl
• [Ne]3s13s2 3s23p13s23p23s23p3 3s23p4 3s23p5
Ar
3s23p6
•
53I:
[He]2s22p2
[Kr]4d105s25p5
6C:
24Cr:
[Ar]4s13d5
The elements of the third period end with Argon. After
argon instead of 3d the next sub-shell to fill is 4s.
The 19. electron of
potassum occupies
4s instead of 3d
orbital since 4s has
lower energy level.
Example: Write out the electron configuration of
[38Sr]+2 and 26Fe ,[26Fe]+2 in the condensed spdf
notation ?
22s22p63s23p64s23d104p65s2
Sr:
1s
38
(according to the order of orbital energy
levels)
38Sr,
Solution
•
22s22p63s23p63d104s24p65s2 (according to the
Sr:
1s
38
increasing principal quantum number “n” )
•
38Sr:
[Kr]5s2 (according to the order with the indication
of noble gas core electron configuration )
• [38Sr]+2: 1s22s22p63s23p63d104s24p6
•
26Fe:
1s22s22p63s23p64s23d6
• [26Fe]+2: 1s22s22p63s23p63d6