1. LECTURE Sixteen CHM 151 ©slg
Topics:
1. Shells, Subshells, Orbitals
2. Electronic Configurations

2. Summation of last points, Lecture 15:
Heisenberg:
Uncertainty Principle: cannot determine simultaneously
the exact location and energy of an electron in atom
Schroedinger:
Wave equation to calculate probable location of e’s
around nucleus using dual matter/wave properties of e’s.
Three quantum numbers from equation locate e’s of
various energies in probable main shells, subshells,
orbitals.

3. The Quantum Numbers
“Locators, which describe each e- about the nucleus
in terms of relative energy and probable location.”
The first quantum number, n, locates each electron
in a specific main shell about the nucleus.
The second quantum number, l , locates the electron in a
subshell within the main shell.
The third quantum number, ml , locates the electron in
a specific orbital within the subshell.

4. Locator #1, “n”, the first quantum number
“n”, the Principal quantum number:
Has all integer values 1 to infinity: 1,2,3,4,...
Locates the electron in an orbital in a main shell
about the nucleus, like Bohr’s orbits
describes maximum occupancy of shell, 2n2.
The higher the n number:
the larger the shell
the farther from the nucleus
the higher the energy of the orbital in the shell.

6. Locator #2, “l”, the second quantum number
locates electrons in a subshell region within the
main shell
limits number of subshells per shell to a value equal to n:
n =1, 1 subshell
n = 2, 2 subshells
n= 3, 3 subshells .....
only four types of subshells are found to be
occupied in unexcited, “ground state” of atom.
These subshell types are known by letter:
“s” “p” “d ” “f”

7. Diagram of available shells and subshells
On the next slide is a schematic representation
of the shells and subshells available for electron
placement within the atom.
Note that the 5th, 6th and 7th types are given
the alphabetical letters following “f”.
None of these types are occupied in the ground
state of the largest known atoms.

8. n = 7
7s (7p 7d f 7g 7h 7i)
Highest,
biggest
n = 6
6s 6p 6d (6f 6g 6h)
n = 5
5s 5p 5d 5f (5g)
n = 4
4s 4p 4d 4f
n = 3
3s 3p 3d
n = 2
2s 2p 1s
n = 1
Lowest energy, smallest shell

9. Locator #3, “ml”, the third quantum number
“ml”, the third quantum number, specifies
in which orbital within a subshell an electron
may be found.
It turns out that each subshell type contains a unique
number of orbitals, all of the same shape and energy.
Main shell subshells orbitals
ml # n#
l #

10. This third number completes the description of where
a electron is likely to be found around the nucleus:
All electrons can be located in an orbital within a subshell within a main shell. To find that electron one need a locating value for each:
the “n” number describes a shell
(1,2,3...)
the “l” number describes a subshell region
(s,p,d,f...)
the “ml” number describes an orbital within the
region
(Each of these quantum numbers has a series of numerical values. We will only use the n number values, 1-7.)

11. The Third Q#, ml continued
“ml” values will describe the number of orbitals within a
subshell, and give each orbital its own unique “address”:
s subshell p subshell d subshell f subshell
1 orbital orbitals orbitals orbitals

12. “l”
“ml” f f f f f f f f d d d d d d p p p p s s

13. It was subsequently discovered that each orbital
we have described is home to not just one but two
electrons, with opposite spins!
We are now treating an electron as a spinning charged
matter particle, rotating clockwise or counterclockwise
on its axis: (next slide)
To describe this situation, a fourth quantum number
is required, the magnetic quantum number, “ms”.

14. As a consequence, we now know:
s subshell, one orbital, 2 e’s
p subshell, three orbitals, 6 e’s,
d subshell, five orbitals, 10 e’s,
f subshell, seven orbitals, 14e’s,

15. This 4th Q# completes the set of “descriptors” or
“locators” needed to assign each electron a unique
position in the arrangement around the nucleus.
Pauli’s Exclusion Principle sums it up: no two e’s in the
same atom, can have the same four Q#’s. .

16. “l”
“ml”
“ms” f d p s

17. 2e’s
6 e’s
10 e’s
14 e’s
s p d f
n = 4
n = 3
n = 2
n = 1

18. Now that we have found places to put our electrons,
in orbitals within subshells within shells, let’s take a
look at the shapes of the various types of orbitals.
The “orbital shapes” are simply enclosed areas of
probability for an electron after a three dimensional
plot is made of all solutions for that electron from the
wave equation.
Each orbital within a subshell is centered about the
nucleus and extends out to the boundaries of its
main shell. Its exact orientation within the subshell
depends on the value of its ml number.

19. Checkout CD-ROM!

20. Energy Description of e’s
The first two quantum numbers, n and l, give
information about the relative energy of electrons
in their location:
As the “n” number increases, the energy of the e
in that shell increases: 1<2<3<4<5<6<7
As the “l” number increases, the energy of the e
in a subshell within the shell increases: s<p<d<f

21. The “ml” number describes the number of orbitals
within a subshell of the same energy.
Accordingly, the relative energy of an electron in
any given orbital within a subshell is given by the
sum of its “n” and “l” numbers.
We have described the following subshells for the
electrons:
1s; 2s, 2p; 3s, 3p, 3d; 4s, 4p, 4d, 4f; 5s, 5p, 5d, 5f;
6s, 6p, 6 d; 7s
Let’s next discuss their relative energy...

22. 2e’s
6 e’s
10 e’s
14 e’s
s p d f
n = 4
= = = 7
n = 3
= = 5
n = 2 =3
n = 1 1

23. Relative energy of subshells
s p d f

24. Order of Filling, Lowest energy to Highest
s p d f
START HERE

25. Low energy
High energy

26. Let’s reorder, starting off with each new shell s subshell:
Is this shape familiar?
1s, 1
< 2s, <2p, 3
< 3s , <3p, 4
< 4s, <3d, <4p, 5
< 5s, <4d, <5p, 6
< 6s, < 4f, <5d, <6p, 7
<7s, <5f, <6d, 8
Let’s expand...

27. THE PERIODIC TABLE, ARRANGED BY SUBSHELLS?
14e’s
6 e’s
2e’s
10 e’s

28. Subshells, relative energy (n + l)
s-block
p-block
d-block
f-block
PERIODS

29. Our next task is to fill electrons around the nucleus into
the orbitals we have described. The electrons will fill
from lowest energy subshell to highest.
The sum of n + l gives us a ranking order of filling
subshells which does not simply progress from
completion of one shell to beginning of another.
However, We will use the periodic table to guide us
quickly through this complex sequence order.

30. Periodic Table as Guide
The periodic table lists all elements sequentially in order of atomic number: this means that each element in turn has one more electron than its predecessor.
We’ll call this electron, the last one to be placed around
the nucleus, the “distinguishing electron”...
We can subdivide the PT into four blocks, showing which
elements have their “distinguishing” or “final” electron
in an “s” or a “p” or a “d” or a “f” type subshell.

31. Where the Final Electron Goes: s,f,d,p Blocks of Elements

32. Subshells by order of filling, Lowest energy to highest

33. GROUP WORK: Complete the following table:
Subshells being filled in each period:
1st Period:
2nd Period :
3rd Period :
4th Period :
5th Period :
6th Period :
7th Period :
Relate subshell numbers to period numbers.

34. KEY!
Subshells being filled in each period:
1st: 1s
2nd: 2s p
3rd: 3s p
4th: 4s d 4p
5th: 5s d 5p
6th: 6s 4f 5d 6p
7th: 7s 5f 6d

35. Conclusions Each period begins with an element filling an e into
the s subshell in a new main shell whose n# is equal to
the period number.
Each period ends with an element completing a p
subshell whose n# is equal to the period number.
s,p: n# = period number

36. ELECTRONIC CONFIGURATIONS OF THE
ELEMENTS
We can now describe the arrangement of all the
electrons around the nucleus of any given atom
in terms of shells and subshells.
We will call these arrangements “electronic
configurations” and they can be done in two modes:
“spectroscopic notation” or “orbital box diagram”

37. 1s1 Let’s consider Hydrogen, Z=1: “spectroscopic notation”
Total e’s in subshell
Main shell
1s1
subshell
“orbital box diagram” 1s

38. THE NEXT 4 ELEMENTS
1s s p

39. HUND’S RULE Following the placement of the first electron into the
p subshell with Boron, the question then becomes,
“does the next electron into the p subshell go to the
second p orbital or does it fill up the first p orbital?”
Hund’s Rule answers that question: in filling
multi-orbital subshells, always put one electron into
each, same spin, then begin filling each “half full”
orbital.

40. 1st, 2nd 3rd electron
in place:
Filling “p” orbitals:
4th electron
in place