Empowering students' understanding of the shell structure of the atom''

The greatest problem in understanding the atomic structure is: the shell structure (ring diagram) and the orbital structure (box diagram), which remain disconnected. The concepts of subshells and orbitals (and suborbitals) is not effectively presented either in the ring diagram or in the box diagram. Quantum numbers are treated as though they are extraneous to the ring diagram or even the box diagram. What has been presented here is a Primer on atomic shell structure.

1. Empowering Students’
Understanding of the
Atomic Shell Structure –Part 1
Shells, Subshells, and Orbitals
B
D
C D
D
Dr. Renuka Rajasekaran
Chemist and Chemistry Educator
PhD (Chemistry); PhD (Chemistry Education)
[email protected]
The greatest problem in understanding the atomic structure is: the shell structure (ring diagram) and
the orbital structure (box diagram), which remain disconnected. The concepts of subshells and
orbitals are not effectively integrated either in the ring diagram or in the box diagram. Quantum
numbers are treated as though they are extraneous to both diagrams. There is not enough emphasis
at the fundamental level, on the fact that the shell structure forms the basis for the periodic table.
Here is a simpler treatment of the atomic structure for the high school students and the early
chemistry courses in college. This Part 1 in the Series.
Progressive Chemistry Learning Series
Volume 1, 2006, pp. 1-7.

2. B
D
C D
D
Shell Names
7th-Q Shell
6th-P Shell
5th-O Shell
4th-N Shell
3rd-M Shell
2nd-L Shell
1st-K Shell
In1913,NeilsBohrproposedtheDiscreteOrbitsModelor
PlanetaryModel.Accordingtothismodel,electronsrevolve
aroundthenucleusincircularorbits,whichlieatfixeddistances
fromthecentralnucleus.Bohr’stheorywasimprovisedbyother
scientistsandthefollowingisasummaryofthose
improvisations:
Shellsaremadeupofsubshellsandsubshellsaremadeupof
orbitals.Itisintheorbitalsthatelectronsreside,Therearefour
kindsofsubshells:S,P,D,andF.Subshellsareimaginaryzones
intheshells.Itisinthesezonesthatorbitalsarepresent.
Orbitalsarelikeapartmentsfortheelectrons.TheSsubshellisa
singleroomapartmentandcontainsonlyoneorbitalcalledthes
orbital.ThePsubshellisathree-roomapartmentandcontainsa
setofthreeorbitalscalledtheporbital.Eachporbitalis
thereforeasetofthreeporbitals;p
x,p
y,andp
z.TheDsubshellis
afive-roomapartmentandcontainsasetoffivedorbitals:
d
z
2
,d
xy,d
xz,d
yz,andd
x
2
-y
2.
TheFsubshellisaseven-room
apartmentandcontainssevenforbitals.
NotethattheSsubshellispresentinallshells,startingfromthe
firstshell.ThePsubshellbeginsonlyinthesecondshellanditis
presentinalltheshellsexceptingthefirstshell.TheDsubshell
beginsonlyinthethirdshellandendsinthesixthshell;thatis,
theDSubshellispresentinthird,fourth,fifth,andsixthshells
andisnotpresentinthe7
th
shell.TheFsubshellbeginsonlyin
thefourthshell.Itendsinthefifthshell.Thatis,theFsubshellis
presentonlyinthefourthandthefifthshells.
See that the D subshell begins in the third
shell and ends in the sixthshell.
See that the F subshell
begins in the fourth shell
and ends in the fifth
shell.
A “P”
subshell is
like a
property
that has a
three-room
apartment
A “S” subshell
is like a property
that has a one-
room apartment
A “D” subshell is like
a property that has a
five-room apartment
A “F” subshell
is like a
property that
has a seven-
room apartment
Eachroomiscalledasuborbital;Eachsuborbitalcan
holdamaximumofTWOelectrons.Eachroomhasa
specificname.thesorbitalhasnosuborbital.
porbital:p
x,p
y,p
z
dorbital:d
xy,d
yz,d
xz,d
x^2-Y^2,d
z^2
Namesofforbitalsarelittlemorecomplexand
arenotrequiredforhighschoolchemistrycourses.
Note: Upper Case –
Lower Case Distinction: S
shell has s orbitals. P
shell has p orbitals. D
shell has d orbitals. F
shell has f orbitals. The
number before the lower
case letter represents the
number of the shell.
Nucleus
1s
ATOMIC STRUCTURE FOUNDATIONS: Ring Diagram of Shell Structure

3. ATOMIC STRUCTURE FOUNDATIONS: Ring Diagram of Shell Structure
A B
D
D
D
Q Shell –one S subshell and one
P subshell –maximum of 8
electrons only
P Shell one S subshell, one P
subshell, and one D subshell –
Maximum of 18 electrons
O Shell -one S subshell, one P
subshell, one D subshell, and
one F subshell –Maximum of 32
electrons
N Shell –one S subshell, one P
subshell, one D subshell, and
one F subshell –Maximum of 32
electrons
M Shell –one S subshell, one P
subshell, and one D subshell –
Maximum of 18 electrons
L Shell –one S subshell and one
P Subshell –Maximum of 8
electrons
K Shell –one S subshell –
Maximum of TWO electrons
Whenfullyfilled,asorbitalwillholdtwo(1x
2=2)electrons;aporbitalwillholdsix
electrons(3x2=6);adorbitalwillhaveten
electrons(5x2=10);andaforbitalwillhave
fourteenelectrons.
SeetheOctetConfigurationoftheValence
Shell,typicalofafullyfilledshellasin
NobleGases.However,rememberthat
Heliumwillhaveonlytwoelectronsinits
valenceshellbecauseitsvalenceshellisthe
firstshellwithamaximumcapacityofonly
twoelectrons.
See that the d orbitals begin
in the third shell and ends in
the penultimate shell.
See that the f orbitals begins in the fourth shell
and ends in the fifth shell. The f orbitals in the 4
th
shell are called 4f orbitals; the f orbitals in the 5
th
shell are called 5f orbitals.
S subshells filled
with electrons in
their one single
orbital per shell
(I x 2 = 2
electrons).
P subshells filled with
electrons in their three
sub orbitals, namely p
x.
P
y,andp
z(3 x 2 = 6
electrons in all, two
per each in the set of
three suborbitals).
F subshells filled
with electrons in
their seven orbitals
(7 x2 =14 electrons
in all, two per each
in the set of seven
sub orbitals).
D subshells filled with
electrons in their five
orbitals (5 x 2 = 10
electrons in all, two
per each in the set of
five suborbitals).
Shell Names
7th-Q Shell
6th-P Shell
5th-O Shell
4th-N Shell
3rd-M Shell
2nd-L Shell
1st-K Shell
Nucleus
1s
2s
3s
4s
5s
6s
7s
2p3p4p5p
6p
7p
3d
4d
5d
6d
4f
5f

4. ATOMIC STRUCTURE FOUNDATIONS: Ring Diagram of Shell Structure
A B
D
D
D
We have already seen that in each orbital can hold two
electrons. How two spinning electrons remain stable and
continue to spin and revolve was a great curiosity.
In order to explain the stability of spinning pairs of electrons in
the orbitals of the shells, Wolfgang Pauli proposed (in 1925)
what is called the Pauli Exclusion Principle, which is given below:
“No two electrons in the same orbital will have all the four
quantum numbers the same. They will differ in the spin quantum
number.”
Theplanetarymodeloftheatomemphasizesthatelectronsare
spinningbodies;thatistheyspinontheirownaxisandalsorevolve
aroundthenucleus.
Shell Names
7th-Q Shell
6th-P Shell
5th-O Shell
4th-N Shell
3rd-M Shell
2nd-L Shell
1st-K Shell
Nucleus
Quantum Numbers are the particulars that describe an electron; in
other words Quantum Numbers are like the address of an
electron. There are four quantum numbers: The Principal
Quantum Number; The Azimuthal Quantum Number; The
Magnetic Quantum Number; and the Spin Quantum Number.
Table 1 provides basic details about quantum numbers.
A detailed discussion on Quantum Numbers is beyond the scope of high school chemistry curriculum.
Some details about the Quantum Numbers are provided in Table 2 as well. However, if you are a high
school student, it is enough if you know that the spin quantum number of electron can be either +1/2
or ─1/2. +1/2 represents the electron spin up (clockwise direction); ─1/2 represents the electron spin
down (counterclockwise direction). We thus understand from the Pauli Exclusion Principle that the two
electrons within the same orbital cannot spin in the same direction but only in the opposite direction)

5. ATOMIC STRUCTURE FOUNDATIONS: Ring Diagram of Shell Structure
B
D
D
D
HowQuantumNumbersWorkisillustrated
hereinTable2.Asalreadystated,forhigh
schoolchemistry,quantumnumbersmaybe
ignored.
Nucleus
1s
spinquantumnumberof
electroncanbeeither
+1/2or─1/2.+1/2
representstheelectron
spinup (clockwise
direction); ─1/2
representstheelectron
spin down
(counterclockwise
direction).
MagneticQuantumNumber
indicateshowmanysuborbitals
(rooms)arepresentinthe
biggestorbitalinthatshell.
Azimuthal quantum
Number(ℓ)tellsyouhow
manysubshellsarepresent
foragivenn
Principal Quantum Number
(n) represents the Shell to
which an electron belongs
Principal Quantum Number
7-Q Shell
6-P Shell
5-O Shell
4-N Shell
3-M Shell
2-L Shell
1-K Shell
Table 2: Understanding Quantum Numbers

6. ATOMIC STRUCTURE FOUNDATIONS: Ring Diagram of Shell Structure
A B
D
D
D
DidyouknowthatthePeriodicTableisbased
ontheShellStructureoftheAtom?
Nucleus
1s

7. The shell structure constitutes the most
fundamental foundation for
understanding the atomic structure.
Also, atomic structure is a growing
concept and runs through curricula
from upper elementary through middle
school to high school, and extends
beyond into college studies and higher
education.
However, students develop very many
misconceptions and struggle through
learning difficulties as they pursue the
atomic structure content presented to
them by text books and other media,
including classroom teaching.
In fact, teachers themselves develop a
lot of misconceptions about atomic
structure and therefore struggle to
present the content effectively to their
students.
The greatest problem in understanding the atomic
structure is: the shell structure (ring diagram) and
the orbital structure (box diagram), which remain
disconnected. The concepts of subshells and
orbitals (and suborbitals) is not effectively
presented either in the ring diagram or in the box
diagram. Quantum numbers are treated as though
they are extraneous to the ring diagram or even
the box diagram.
What has been presented here is a
Primer on atomic shell structure.
Follow the Progressive Chemistry
Learning Seriesto access the other
parts.
Progressive Chemistry Learning Series, Volume 1, 2006, pp. 1─7.