Transcript The energy

Unit 4 –
Quantum Mechanics
Cartoon courtesy of NearingZero.net
Light and Energy
• Much of what we know about electrons
comes from study of light
– Light behaves as waves
– Light also behaves as particles (photons)
Wave properties
• Light waves are part of the
electromagnetic spectrum
• Can be characterized by 5 properties:
–
–
–
–
–
Amplitude
Wavelength
Frequency
Speed
Energy
Electromagnetic radiation propagates
through space as a wave moving at the
speed of light.
c = 
C = speed of light, a constant (3.00 x 108 m/s)
 = frequency, in units of hertz (hz, /s, s-1)
 = wavelength, in meters
Types of electromagnetic radiation:
Calculating the color of light…
• Given that a beam of light has
frequency of 6.0 x 1014 /s
• what is the wavelength of this light?
• What color is it?
(Refer to an electromagnetic spectrum
diagram like the one on p.129)
The energy (E ) of electromagnetic radiation
is directly proportional to the frequency ()
of the radiation. This is the energy of a
photon of a particular frequency.
E = h
E = Energy, in units of Joules (kg·m2/s2)
h = Planck’s constant (6.63 x 10-34 J·s)
 = frequency, in units of hertz (hz, /s, s-1)
Long
Wavelength
=
Low Frequency
=
Low ENERGY
Short
Wavelength
=
High Frequency
=
High ENERGY
Wavelength Table
Spectroscopic analysis of the visible spectrum…
(such as seen from an incandescent light bulb)
…produces all of the colors in a “continuous spectrum”
Spectroscopic analysis of the hydrogen spectrum…
(as given off by a hydrogen gas-filled fluorescent
light bulb)
…produces a “bright line” or “emission spectrum”
Electron transitions
occur when
electrons absorb
energy in a
‘quantum jump’ to an
‘excited state’.
When they ‘fall’
back to their ’
‘ground state’
they emit photons of
light with distinct
wavelengths, visible
as bands on an
‘emission spectrum’
(not all are in the
visible range).
VISIBLE
JUMPS
The Bohr Model of the Atom
I pictured
electrons orbiting
the nucleus much
like planets
orbiting the sun.
Neils Bohr
But it turns out
they’re more
like bees around
a hive.
WRONG!!!
Quantum Mechanical
Model of the Atom
Mathematical laws were used to identify the
regions outside of the nucleus where electrons
are most likely to be found.
These laws are beyond the scope of this class…
But here are two important examples:
Schrodinger Wave Equation

d
h

V 
8  m dx
2
2
2
2
 E
Equation for probability of a
single electron being found
along a single axis (x-axis)
Erwin Schrodinger
Heisenberg Uncertainty Principle
“One cannot simultaneously
determine both the position
and momentum of an electron.”
You can find out where the
electron is, but not where it
is going.
Werner
Heisenberg
OR…
You can find out where the
electron is going, but not
where it is!
Electron Energy Level (Shell)
Generally symbolized by n, it denotes the
average distance of the electron from the
nucleus.
Number of electrons
that can fit in a shell:
2n2
1 holds 2
2 holds 8
3 holds 18 etc.
An orbital is a region within an energy level where
there is a probability of finding an electron. This is a
probability diagram for the…
s orbital…
in the first energy level.
Orbital shapes are defined as the space that
contains the electron 90% of the time.
Quantum Numbers: Electron Addresses!
1st: Energy Level (n = 1, 2, 3, 4 …) Average distance of
the electron in the electron cloud from the nucleus.
2nd: Sublevel (l = s, p, d, f) Shape of electron cloud.
energy levels have n sublevels.
3rd: Orbital (ml) Orientation of the cloud in 3-D space.
s sublevels have 1 orbital
(spherical)
p sublevels have 3 orbitals (dumb bell shape)
d sublevels have 5 orbitals (varied)
f sublevels have 7 orbitals (varied)
4th: Spin (ms = +1/2 or -1/2) Direction of electron spin.
Each orbital holds 2 electrons, one with each spin.
Pauli Exclusion Principle: Each electron
of an atom has its own unique set of
quantum numbers. They may have three
that are the same, but never all four.
Sizes of s orbitals
Orbitals of the same shape (s, for instance) grow
larger as n increases…
Nodes are regions of low probability within an
orbital.
The s orbital
has a spherical shape centered around
the origin of the three axes in space
There is only one orientation for
this shape
P orbital shape
There are three dumbbell-shaped p orbitals in
each energy level above n = 1, each assigned to
its own axis (x, y and z) in space.
Things get a bit more
d orbital shapescomplicated with the
five d orbitals that
are found in the d
sublevels beginning
with n = 3.
To remember the
shapes, think of
“double dumbells”
…and a “dumbell
with a donut”!
In case you are too curious, here
is what the f orbitals look like.
Energy Levels, Sublevels, Electrons
Energy
Level
(n)
Sublevels in
main energy
level
(n sublevels)
Number of
orbitals per
sublevel
Number of
Electrons
per sublevel
Number of
electrons per
main energy
level (2n2)
1
s
1
2
2
2
s
p
1
3
2
6
8
s
p
d
1
3
5
2
6
10
18
s
p
d
f
1
3
5
7
2
6
10
14
32
3
4
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p67s25f14…
The Diagonal Rule: Sublevels in
order of increasing energy
5g18
4f14 5f14 6f14
3d10 4d10 5d10 6d10 7d10
2p6 3p6 4p6 5p6 6p6 7p6 8p6
1s2 2s2 3s2 4s2 5s2 6s2 7s2 8s2
Aufbau Principle: Electrons fill the lowest
energy position available.
Energy levels and sublevels on
the Periodic Table
Hund’s Rule: Electrons fill orbitals so
that there are a maximum number of
orbitals with a single electron.
Element
Lithium
Configuration
notation
1s22s1
[He]2s1
____
1s
Beryllium
____
____
2p
____
____
2s
____
____
2p
____
[He]2s2p2
____
2s
____
____
2p
____
1s22s22p3
[He]2s2p3
____
2s
____
____
2p
____
1s22s22p4
[He]2s2p4
____
2s
____
____
2p
____
1s22s22p5
[He]2s2p5
____
1s
Neon
____
2s
1s22s22p2
____
1s
Fluorine
____
[He]2s2p1
____
1s
Oxygen
____
2p
1s22s22p1
____
1s
Nitrogen
____
[He]2s2
____
1s
Carbon
____
2s
1s22s2
____
1s
Boron
Noble gas
notation
Orbital notation
____
2s
____
____
2p
____
1s22s22p6
[He]2s2p6
____
1s
____
2s
____
____
2p
____
Electron configuration of the
elements of the first three periods