Transcript document

LECTURE Sixteen
CHM 151 ©slg
Topics:
1. Shells, Subshells, Orbitals
2. Electronic Configurations
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.
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.
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.
"n" MAIN SHELLS ABOUT THE NUCLEUS
7
6
5
4
3
2
1
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”
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.
n=7
7s
(7p 7d
7f
7g 7h 7i)
n=6
6s
6p
6d
(6f 6g 6h)
n=5
5s
5p
5d
5f
n=4
4s
4p
4d
4f
n=3
3s
3p
3d
n=2
2s
2p
n=1
1s
Highest,
biggest
(5g)
Lowest energy, smallest shell
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
n#
subshells
l#
orbitals
ml #
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.)
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
1 orbital
3 orbitals
5 orbitals
f subshell
7 orbitals
“l”
f
d
p
s
“ml”
f
f
f
f
d
d
d
d
p
p
p
s
f
f
f
d
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”.
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,
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. .
“l”
f
d
p
s
“ml”
“ms”
n=4
n=3
n=2
n=1
2e’s
6 e’s
10 e’s
14 e’s
s
p
d
f
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.
all s orbitals
all p orbitals
d orbitals
Checkout CD-ROM!
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
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...
2e’s
6 e’s
10 e’s
14 e’s
s
p
d
f
n=4
4
4+1 =5
4+2=6
3
3+1 =4
3+2=5
2
2+1 =3
n=3
n=2
n=1
1
4+3=7
Relative energy of subshells
s
p
d
f
n=7
7
n=6
6
7
8
n=5
5
6
7
8
n=4
4
5
6
7
n=3
3
4
5
n=2
2
3
n=1
1
Order of Filling, Lowest energy to Highest
s
p
d
f
n=7
7
n=6
6
7
8
n=5
5
6
7
8
n=4
4
5
6
7
n=3
3
4
5
n=2
2
3
n=1
1
START HERE
Low energy
1s, 1
< 2s,2
< 2p, 3 < 3s,3
<3p, 4 <4s, 4
<3d, 5 < 4p, 5
<4d,6
<5s, 5
<5p, 6 <6s,6
< 4f, 7 <5d,7 <6p,7 <7s, 7
<5f, 8
<6d, 8
High energy
Let’s reorder, starting off with each new shell s subshell:
Is this shape familiar?
1s, 1
< 2s, 2
<2p, 3
< 3s ,3
<3p, 4
< 4s, 4
<3d, 5
<4p, 5
< 5s, 5
<4d, 6
<5p, 6
<6p, 7
< 6s, 6
< 4f, 7
<5d, 7
<7s, 7
<5f, 8
<6d, 8
Let’s expand...
THE PERIODIC TABLE, ARRANGED BY SUBSHELLS?
1
2
1s,1
2p,3
2s,2
14e’s
3
3s,3
4
4s,4
3d, 5
5
5s,5
4d,6
6
6s,6
4f,7
5d, 7
7
7s,7
5f,8
6d,8
2e’s
3p, 4
4p,5
5p,6
6p,7
10 e’s
6 e’s
Subshells, relative energy (n + l)
s-block
p-block
1
2
1s,1
d-block
2p,3
2s,2
f-block
3p, 4
3
3s,3
4
4s,4
3d, 5
5
5s,5
4d,6
6
6s,6
4f,7
5d, 7
7
7s,7
5f,8
6d,8
PERIODS
4p,5
5p,6
6p,7
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.
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.
Where the Final Electron Goes:
s,f,d,p Blocks of Elements
s
p
d
f
Subshells by order of filling,
Lowest energy to highest
1s
1s
2s 2s
2p 2p 2p 2p 2p 2p
3s 3s
3p 3p 3p 3p 3p 3p
4s 4s
3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 4p 4p 4p 4p
5s 5s
4d 4d 4d 4d 4d 4d 4d 4d 4d 4d 5p 5p 5p 5p 5p 5p
6s 6s 4f
5d 5d 5d 5d 5d 5d 5d 5d 5d 5d 6p 6p 6p 6p 6p 6p
7s 7s 5f
4p 4p
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.
KEY!
Subshells being filled in each period:
1st: 1s
2nd: 2s
2p
3rd: 3s
3p
4th: 4s
3d 4p
5th:
5s
4d 5p
6th:
6s 4f 5d 6p
7th:
7s 5f 6d
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
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”
Let’s consider Hydrogen, Z=1:
“spectroscopic notation”
Total e’s in subshell
Main shell
1s1
subshell
“orbital box diagram”
1s
THE NEXT 4 ELEMENTS
He
Li
Be
B
Z=2
1s2
Z=3
2
1s 2s
1
Z=4
2
1s 2s
2
Z=5
2
2
1s 2s 2p
1
1s
2s
2p
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.
Filling “p” orbitals:
4th electron
in place
1st, 2nd 3rd electron
in place: