Transcript Chapter 6: Part 2 - The Bronx High School of Science

Chapter 6: Part 2
…because microsoft 2003 is terrible.

Do Now:
◦ Have out your homework for me to come and
check.
◦ Complete the following Problem:
 Using the Equation for change in energy calculate
the energy at n = 2 and n = 6. Calculate the
wavelength of the radiation released when an
electron moves from n = 6 to n = 2.
December 14th, 2012
Take a Look at this!

Proposed that the dual
nature of matter places
fundamental limitation
on how precisely we can
know both the location
and momentum at any
given instant.

Limitation is very small
for large objects, very
large for small. **YIKES!
HOW SMALL IS AN ELECTRON AGAIN?!**
Heisenberg, Heisenberg, he’s our man! If he
can’t find it… well, odds are, it can’t be
found.
D x  D  mv  
•
•
•
•
h
4
Dx = uncertainty of position
Dmv = uncertainty of momentum
h = Planck’s constant
The more accurately we know a particle’s
position, the less accurately we can know its
momentum.
Mathematically Speaking…

Organize Heisenberg’s equation so that
the uncertainty of momentum is what we
are solving for… **forget the greater than
sign… set it as equal.
h
h
How is the
D  mv 

uncertainty of
4D x 4 (0)
momentum
effected as the
uncertainty of
position
approaches 0?
To infinity and beyond!
Wave – particle duality

Erwin Schrödinger
◦ Created equation that incorporates both wave
behavior and particle behavior
d
 2
 V  E
2
8 m dx
h
2
2
◦ Solving this equation leads to a series of
functions called wave functions (represented by
psi)
◦ Ψ itself has no function, Ψ2 provides
information about an electrons location when in
an allowed state
Quantum Mechanics
According to uncertainty principle if we
know the momentum of the electron with
high accuracy, our simultaneous
knowledge of location is very uncertain.
 We must be content speaking of
probability.
 Ψ2 called probability density or electron
density

…probably??
Location, Location, Location!

Total of four quantum numbers- developed to
better understand path and movement of
electrons.

Each indicates a trait of an electron within the
atom to help explain wave functions.

No 2 electrons can share came combination of
four quantum numbers.

They are very significant because they can
determine the electron configuration of an atom
and a probable location of the atom's electrons.
Orbitals and Quantum Numbers
n
“principle quantum number”
Can have positive integral values 1infinity
 Increase in n, orbital becomes larger,
less time spent near nucleus
 Increase in n= higher energy, less
tightly bound to nucleus
 Collection of orbitals within “n” is called
electron shell


n is for eNergy
l
“azimuthal quantum number”
 Integral values from 0 to n-1 for each value of n
 Defines the shape of the orbital (s,p,d,f –
corresponds to the value of l)

l is for anguLar momentum
 can
ml
have integral values of –l to l,
including zero.
 Describes orientation of orbital in
space
m is for Magnetic quantum
number

If n can be any positive integer, how
many possible energy levels can any atom
have?
◦ Occupied vs. unoccupied
…I’m running out of good titles

Collection of orbitals with same value “n”
is called electron shell.
◦ IE: 3s, 3p, 3d

Orbitals that have same “n” and “l” values
are called subshells
◦ IE: orbital that has n= 3 and l= 2 are called 3d orbitals
and are in 3d subshell

“n” designates # of subshells.
◦ IE: n= 2 means 2 subshells= 2s and 2p
Break it down now…
Each Box
represents 1
orbital.
Therefore:
n=1 shell, 1
orbital
n= 2 shell= 2
subshells, 4
orbitals
NRG.
DO NOW:
 Without referencing previous slide, predict
the number of subshells in the fourth shell
(n=4).
◦ Give a label to each of these subshells
◦ How many orbitals are in each of these subshells?

What is the designation for the subshell with
n=5 and l=1.
◦ How many orbitals are there in this subshell?
◦ Indicate the values of ml for each of these orbitals.
December 18th, 2012
“s”
Describe the “s”
orbitals.
Spherically symmetric
Electron density at a given distance from the nucleus
is same regardless of direction.
 How do they differ as the n value changes?


Orbitals, REPRESENT!

“Radial probability density”
◦ Probability that we will find the electron at a
specific distance from the nucleus
What are
three trends
you observe
on this graph?
TALK WITH
YOUR
NEIGHBOR.
Radial Probability Function
Concentrated in 2 regions on either side of nucleus
(two lobes)
 Averaged distribution of electron density in “p”
orbital.
 Each has p has 3 orbitals
 Higher value “n”, larger the p orbital

p-lease tell me how the p looks!
d occurs @ n= 3
or greater
 Five d orbitals
per subshell
 “four leaf clover”
 All d orbitals
have same
energy

d-on’t go breakin’ my heart! Tell
me about the d!
n= four or greater
 seven f orbitals per subshell.

f-rightening!


Any atom beyond Hydrogen
Shapes are the same as hydrogen,
presence of more than 1 electron changes
energies
◦ Electron-electron repulsion cause subshells to
be at different energy levels (more in chapter
7)

For same values of n (3s, 3p, 3d) energy
increases with increasing value of l.
◦ 3s < 3p< 3d
“many” electron atoms
All “orbitals” of a given
subshell have same
energy
Orbitals with same
energy are called
“degenerate”
Qualitative Energy Diagram
DO NOW:
 How do you denote the location of n = 3 l
=1
 How do you denote the location of n= 4
l=2
 How many possible orbitals are found in
the d subshell?
December 19th, 2012




How do electrons of
multi-electron atom
populate available
orbitals?
Line spectraoriginally thought to
be 1 line, actually 2.
Why?
2 possible values:
+1/2 or -1/2 (2
opposite directions of
spin)
2 possible directions
cause opposite
magnetic fields.
Spinning. (ms)

Wolfgang Pauli (1925)
◦ Principle that governs arrangement of electrons
◦ No 2 electrons can have same set of 4
quantum numbers
◦ Only 2 ms values, therefore only 2 electrons
per orbital
◦ Essentially, IP address for an electron
Pauli Exclusion Principle




Way electrons are distributed among various
orbitals of an atom
If there were no restrictions on possible
values of quantum numbers, where might the
electrons crowd? Why?
Orbitals fill in order of increasing energy, no
more than 2 electrons per orbital
We represent electron config. By writing
symbol for occupied subshell and adding
superscript to indicate number of electrons in
subshell. IE:
Electron Configuration




Which element is represented here?
Each orbital denoted by a box and electron by
half arrow. (arrow up = positive spin, arrow
down= negative)
If electrons of opposite spins are together=
paired.
Unpaired = single electron.
Orbital Diagrams
Stable Configurations = configurations
with full orbitals
 Where do we place electrons when we get
to the 2p subshell?

◦ Why does it not matter where we place the first
electron in the 2p subshell?
 SAME ENERGY

Where does the second electron in the 2p
subshell go?
Hunds Rule

HUNDS RULE: for degenerate orbitals,
lowest energy is attained when the
number of electrons having the same
spin is maximized.
ELECTRONS
ARRANGED
THIS WAY
HAVE
“PARALLEL
SPINS”
HAVE THE
LOWEST
POSSIBLE
ENERGY!
“PARALLEL
SPINS”
HUNDS RULE (for real this time)
Why do you think electrons remain
unpaired?
 How does this lower the energy in the
atom?

Why?
 Write
the electron configuration
for phosphorus, element 15
 How many unpaired electrons
does phosphorus have?
Practice
DO NOW:
 Write the electron configuration for
Strontium
 Write the electron configuration for
Cadmium
 Write the electron configuration for
Tellurium
December 20th, 2012





Where is the filling of the 2p orbital
complete?
How can we condense sodiums electron
configuration?
Define condensed electron configuration.
How do we differ between core electrons
and valence electrons?
Why are these useful?
Condensed Configurations




Where are these 2 groups located?
[Rn]7s26d1 – Which element is represented
by this electron configuration?
Which orbitals are being filled by the
lanthanides and actinide series?
Why are there no elements above the
lanthanide and actinide series?
◦ Electrons in completely filled d or f subshells
are not considered valence electrons
Lanthanides and Actinides
What is the electron configuration of
Holmium
 What is the electron configuration of
Americium
 What is the electron configuration of
Xenon

Practice- YEEHEE!

How does the periodic table relate directly
to the filling of the orbitals?
Electron Configuration and the
P.T.
How do the number of columns in each
block correspond to the maximum
number of electrons that occupy each
subshell?
 Lets take a look at a trick…

How can we
shortcut
determining
electron
config?
…Ohhh…
What family of elements if characterized
by an ns2np2 electron configuration in the
outermost occupied shell?
 Based on its position on the periodic
table, write the condensed electron
configuration for bismuth, element 83.

◦ How many unpaired electrons does bismuth
have?
Practice

Certain electron configurations appear to
violate rules
◦ Groups 6 and 11

Due to closeness of 3d and 4s orbital
energies.
Anomalous Electron Configuration