progression of the concept of "orbitals within shells"

Empowering Students’ Understanding of the

Atomic Shell Structure – Part 1Shells, Subshells, and OrbitalsB

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C D

D

Dr. Renuka RajasekaranChemist and Chemistry EducatorPhD (Chemistry); PhD (Chemistry Education)

[email protected] greatest problem in understanding the atomic structure is: the shell structure (ring diagram) and the orbital structure (box diagram) 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 SeriesVolume 1, 2006, pp. 1-7.

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Shell Names7th-Q Shell6th-P Shell5th-O Shell4th-N Shell3rd-M Shell2nd- L Shell1st- K Shell

In 1913, Neils Bohr proposed the Discrete Orbits Model or Planetary Model. According to this model, electrons revolve around the nucleus in circular orbits, which lie at fixed distances from the central nucleus. Bohr’s theory was improvised by other scientists and the following is a summary of those improvisations:Shells are made up of subshells and subshells are made up of orbitals. It is in the orbitals that electrons reside, There are four kinds of subshells: S, P, D, and F. Subshells are imaginary zones in the shells. It is in these zones that orbitals are present. Orbitals are like apartments for the electrons. The S subshell is a single room apartment and contains only one orbital called the s orbital. The P subshell is a three-room apartment and contains a set of three orbitals called the p orbital. Each p orbital is therefore a set of three p orbitals; px, py, and pz. The D subshell is a five-room apartment and contains a set of five d orbitals: dz

2, dxy, dxz, dyz , and dx2

-y2. The F subshell is a seven-room

apartment and contains seven f orbitals.

Note that the S subshell is present in all shells, starting from the first shell. The P subshell begins only in the second shell and it is present in all the shells excepting the first shell. The D subshell begins only in the third shell. The F subshell begins only in the fourth shell.

See that the D subshell begins in the third shell and ends in the penultimate shell.

See that the F subshell begins in the fourth shell and ends in the antepenultimate 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

Each room is called an orbital; Each orbital can hold a maximum of TWO electrons. Each room has a specific name.p orbital: px, py, pz

d orbital: dxy, dyz, dxz, dx^2-Y^2, dz^2

Names of f orbitals are little more complex and are not required for high school chemistry courses.

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

1s2s3s

4s5s

6s7s

7p4f

5f

6p5p 4p3p

2p

4d

3d

5d6d

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 onlyP Shell one S subshell, one P subshell, and one D subshell – Maximum of 18 electronsO Shell - one S subshell, one P subshell, one D subshell, and one F subshell – Maximum of 32 electronsN Shell – one S subshell, one P subshell, one D subshell, and one F subshell – Maximum of 32 electronsM Shell – one S subshell, one P subshell, and one D subshell – Maximum of 18 electronsL Shell – one S subshell and one P Subshell – Maximum of 8 electrons K Shell – one S subshell – Maximum of TWO electrons

When fully filled, a s orbital will hold two (1 x 2 = 2) electrons; a p orbital will hold six electrons (3 x 2 = 6); a d orbital will have ten electrons (5 x 2 = 10); and a f orbital will have fourteen electrons.

See the Octet Configuration of the Valence Shell, typical of a fully filled shell as in Noble Gases. However, remember that Helium will have only two electrons in its valence shell because its valence shell is the first shell with a maximum capacity of only two electrons.

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 antepenultimate shell. The f orbitals in the 4th shell are called 4f orbitals; the f orbitals in the 5th shell are called 5f orbitals.

S subshells filled with electrons in their one single orbital per shell (I x 2 = 2 electrons in all per orbital).

P subshells filled with electrons in their three orbitals (3 x 2 = 6 electrons in all per the set of three orbitals per subshell.

F subshells filled with electrons in their seven orbitals (7 x2 =14 electrons in all per the set of seven orbitals).

D subshells filled with electrons in their five orbitals (5 x 2 = 10 electrons in all per the set of five orbitals).


Nucleus

1s2s

3s4s

5s

6s7s

2p3p4p5p6p7p

3d

4d

5d

6d

4f

5f


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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.”

The planetary model of the atom emphasizes that electrons are spinning bodies; that is they spin on their own axis and also revolve around the nucleus.


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)


B

D

D

D

How Quantum Numbers Work is illustrated here in Table 2. As already stated, for high school chemistry, quantum numbers may be ignored.

Nucleus

1s2s

3s4s

5s6s

7s

2p3p4p5p6p

7p

4f

5f

3d

4d5d

6d

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).

Magnetic Quantum Number indicates how many rooms are present in the biggest orbital in that shell.

Azimuthal quantum Number (ℓ) tells you how many subshells are present for a given n

Principal Quantum Number (n) represents the Shell to which an electron belongs

Principal Quantum Number7-Q Shell6-P Shell5-O Shell4-N Shell3-M Shell2- L Shell1- K Shell

Table 2: Understanding Quantum Numbers


A B

D

D

D

Did you know that the Periodic Table is based on the Shell Structure of the Atom?

NucleusRe

pres

enta

tive

elem

ents

S Block Elements:

Alkali M

etals

and Alkalin

e Earth

Metals

p Bl

ock

Elem

ents

: Bor

on

Fam

ily to

Nob

le G

ases

d Block Elements:

Transition Elements

f Block Elements: Inner

Transition Elements

1s2s

3s4s

5s6s

7s

2p3p4p5p6p

7p

4f

5f

3d

4d5d

6d

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 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) remain disconnected. The concepts of subshells and orbitals 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 Series to access the other parts.

Progressive Chemistry Learning Series, Volume 1, 2006, pp. 1─7.