Transcript Chapter 6: Electronic Structure

Chapter 7: Electronic Structure
Electrons in an atom determine virtually
all of the behavior of the atom.
 Quantum theory – the study of how
energy and matter interact on an atomic
level.
 To understand the electron, we must first
understand light.
 Reason =

Light
Also known as electromagnetic radiation.
 Ex) Visible light, Infrared, X-ray, Radio.
 All electromagnetic radiation have several
common characteristics.

◦ Light as a wave
◦ Light as a particle
◦ “Duality of Light”
Electromagnetic Radiation
Light as a Wave
Wavelength (l – lambda) =
 Frequency (n – nu) =

Light as a Wave
•Wavelength and Frequency are inversely related.
Electromagnetic Spectrum

Shows the full range of electromagnetic
radiation that exists.
Light as a Wave
The product of the wavelength and the
frequency, though, is a constant.
 c = l  n, where c is the speed of light.
 Thus, if we know the frequency, we can
find the wavelength and vice versa.
 LEP #1(a).

Proof of Waves
Waves exhibit certain properties when
they interact with each other.
 Young’s Double Slit experiment.

Proof of Waves
Proof of Waves
Light as a Particle
The wave nature of light
does not explain all of
the properties of light.
 Blackbody radiation –
when solids are heated,
they will glow.
 Color depends on the
temperature.

Light as a Particle
Max Planck – proposed a theory that
energy from blackbody radiation could
only come in discrete “chunks” or quanta.
E=hn
 h = 6.626 x 10-34 Js
 LEP #1(b).

Light as a Particle
The photoelectric
effect (Einstein)
also is proof that
light must have a
tiny mass and thus
act as a particle
(photon).
 LEP #2, #3.

Line Spectra

When a gas like
H2, Hg, or He is
subjected to a
high voltage, it
produces a line
spectrum
consisting of
specific
wavelengths.
Line Spectra
High Voltage Excitation
Identifying Metals
Na = yellow
K = violet
Li = red
Ba = pale green
Line Spectra

The four lines for hydrogen were found
to follow the formula:
 1
1
1 
7
= 1.097  10 / m   2 - 2 
λ
 nf ni 

Where the values of n are integers with
the final state being the smaller integer.
Bohr Theory
How could such a simple equation work?
 Niels Bohr some thirty years later came
up with a theory.
 Classic physics would predict that an
electron in a circular path should
continuously lose energy until it spiraled
into the nucleus.

Bohr Theory
1.
2.
An electron can only
have precise energies
according to the formula:
E = -RH / n2 ; n = 1, 2, 3,
etc. and RH is the
Rydberg constant.
An electron can travel
between energy states
by absorbing or releasing
a precise quantity of
energy.
Bohr Theory
Bohr Theory
Can not explain the line spectra for other
elements due to electron-electron
interactions.
 Thus, the formula for Hydrogen can only
be applied for that atom.
 LEP #4.

Matter as a Wave

Louis de Broglie proposed that if light
could act as both a wave and a particle,
then so could matter.
h
λ=
mv
Where h is Planck’s constant, m is the
objects mass, and v is its velocity.
 Size, though, matters. LEP #5.

Matter as a Wave
De Broglie was later proven correct when
electrons were shown to have wave properties
when they pass through a crystalline substance.
 Electron microscope picture of carbon
nanotubes.

Uncertainty Principle
German scientist Werner
Heisenberg proposed his
Uncertainty Principle in
1927.
 History

Uncertainty Principle

For a projectile like a bullet, classic physics has
formulas to describe the motion – velocity and
position – as it travels down range.
Uncertainty Principle

Any attempt to observe a single electron
will fail.
Uncertainty Principle
If you want to measure length, there is always
some uncertainty in the measurement.
 To improve the certainty, you would make a
better measuring device.
 Heisenberg, though, stated that the precision
has limitations.
Dx  mDv  h / 4p

Uncertainty Principle
Once again, size
makes a big
difference.
 LEP #6

Uncertainty Principle

Determinacy vs. Indeterminacy

According to classical physics, particles move in
a path determined by the particle’s velocity,
position, and forces acting on it
◦ determinacy = definite, predictable future

Because we cannot know both the position and
velocity of an electron, we cannot predict the
path it will follow
◦ indeterminacy = indefinite future, can only predict
probability
Uncertainty Principle
Quantum Mechanics
The quantum world is very different from
the ordinary world.
 Millions of possible outcomes and all are
possible!
 Quantum Café
 “I am convinced that He (God) does not
play dice.” Albert Einstein

Hy = Ey
Erwin Shrödinger proposed an equation
that describes both the wave and particle
behavior of an electron.
 The mathematical function, y, describes
the wave form of the electron. Ex) a sine
wave.
 Squaring this function produces a
probability function for our electron.

Atomic Orbitals
A graph of y2 versus the radial distance
from the nucleus yields an electron
“orbital”.
 An “orbital” is a 3D shape of where an
electron is most of the time.
 An “orbital” can hold a maximum of two
electrons.

Atomic Orbitals

The Probability density function
represents the probability of finding the
electron.
Atomic Orbitals
•A radial distribution plot represents the total
probability of finding an electron within a thin
spherical shell at a distance r from the nucleus
•The probability at a point decreases with
increasing distance from the nucleus, but the
volume of the spherical shell increases
Atomic Orbitals

The net result for the
Hydrogen electron is a most
probable distance of 52.9pm.
Atomic Orbitals
For n=2 and beyond, the orbital will have
n-1 nodes.
 A node is where a zero probability exists
for finding the electron.

Atomic Orbitals
 2s orbital = 1 node
3s orbital = 2 nodes 
Quantum Numbers

1.
An electron can be described by a set of
four unique numbers called quantum
numbers.
Principle quantum number, n = describes
the energy level of the electron. As n
increases so does the energy and size of
the orbital. n can have values of integers
from 1 to infinity.
Quantum Numbers
2.
Azimuthal quantum number, l, defines
the shape of the orbital. The possible
values of l depends on n and can be all
of the integers from 0 to n-1. However,
the values of 0, 1, 2, and 3 have letter
designations of s, p, d, and f, respectively.
Quantum Numbers
3.
Magnetic quantum number, ml describes
the orientation in space of the orbital.
The possible values of this quantum
number are –l  0  +l. When l is
not zero, the magnetic q.n. has more
than one value. These multiple values
produce degenerative orbitals – orbitals
of equal energy.
Quantum Numbers
4.
Spin quantum
number, ms
describes the
electron spin of
the electron. This
value is either
+1/2 or –1/2.
Quantum Numbers
Quantum Numbers
Pauli Exclusion Principle – no electron in
an atom can have the same set of four
quantum numbers.
 Ne = 10 electrons
 LEP #7.

Subshell Designations
Value
of
l
0
1
2
3
Type
of
orbital
s
p
d
f
Orbitals

s type
orbitals are
spherical in
shape.
Orbitals

p type orbitals have two lobes.
Orbitals

d type orbitals generally have four lobes.