Download The Wave Nature of Light

The Wave Nature of Light
Waves
• To understand the electronic structure of
atoms, one must understand the nature of
electromagnetic radiation.
• The distance between corresponding points
on adjacent waves is the wavelength ().
Waves
• The number of waves
passing a given point per
unit of time is the
frequency ().
• For waves traveling at
the same velocity, the
longer the wavelength,
the smaller the
frequency.
Electromagnetic Radiation
• All electromagnetic
radiation travels at the
same velocity: the
speed of light (c),
3.00  108 m/s.
• Therefore,
c = 
The Nature of Energy
• The wave nature of light
does not explain how
an object can glow
when its temperature
increases.
• Max Planck explained it
by assuming that
energy comes in
packets called quanta.
The Nature of Energy
• Einstein used this
assumption to explain the
photoelectric effect.
• He concluded that energy
is proportional to
frequency:
E = h
where h is Planck’s
constant, 6.63  10−34 J-s.
The Nature of Energy
• Therefore, if one knows the
wavelength of light, one
can calculate the energy in
one photon, or packet, of
that light:
c = 
E = h
The Nature of Energy
Another mystery
involved the emission
spectra observed
from energy emitted
by atoms and
molecules.
The Nature of Energy
• One does not observe
a continuous
spectrum, as one gets
from a white light
source.
• Only a line spectrum of
discrete wavelengths
is observed.
The Nature of Energy
•
Niels Bohr adopted Planck’s
assumption and explained
these phenomena in this
way:
1. Electrons in an atom can only
occupy certain orbits
(corresponding to certain
energies).
The Nature of Energy
•
Niels Bohr adopted Planck’s
assumption and explained
these phenomena in this
way:
2. Electrons in permitted orbits
have specific, “allowed”
energies; these energies will
not be radiated from the atom.
The Nature of Energy
•
Niels Bohr adopted
Planck’s assumption and
explained these
phenomena in this way:
3. Energy is only absorbed or
emitted in such a way as to
move an electron from one
“allowed” energy state to
another; the energy is
defined by
E = h
The Nature of Energy
The energy absorbed or emitted
from the process of electron
promotion or demotion can be
calculated by the equation:
E = −RH (
1
1
- 2
nf2
ni
)
where RH is the Rydberg
constant, 2.18  10−18 J, and ni
and nf are the initial and final
energy levels of the electron.
The Wave Nature of Matter
• Louis de Broglie posited that if light can
have material properties, matter should
exhibit wave properties.
• He demonstrated that the relationship
between mass and wavelength was
h
 = mv
Atomic Electron Configurations
Electron spin
1. Quantum number (ms) – electron
spin magnetic quantum number
2. To totally understand this, we must
first learn about magnetism.
Paramagnetism and Unpaired
Electrons
Substances are:
Diamagnetic if they are repelled by a
strong magnet
Paramagnetic if they are attracted by a
magnet
Electron spins
1. Paramagnetism arises from electron
spins.
2. Electron spins have 2 orientations
3. Therefore, the electron spin is quantized
and can have a quantum number
4. Possible values: ms = + ½ or – ½
Paramagnetism and
diamagnetism
• Paramagnetism occurs in substances in
which the ions or atoms have unpaired
electrons
• Diamagnetism occurs in substances in
which the ions or atoms have paired
electrons
Pauli Exclusion Principle
• No two electrons in an atom can have the
same set of four quantum numbers.
• No atomic orbital can contain more than
two electrons.
What are the possible
numbers of electrons in….
The s orbitals:
The p orbitals:
The d orbitals:
The f orbitals:
2
6
10
14
Aufbau Principle
• Electrons are placed in the lowest
energetically available subshell.
• An orbital can hold at most 2 electrons.
• If two or more energetically equivalent
orbitals are available (e.g., p, d etc.)
then electrons should be spread out
before they are paired up (Hund's rule).
Atomic energy diagram
Which of the subshells should
be filled first?
Order of orbital filling
Types of Notations and
Valence Electrons
• 3 types:
Electron Configuration
Na:
Noble gas notations
Na:
Orbital notations
Exceptions to the Rule
• Cr
• Cu
Electron configurations of ions
(excited state)
• Rules:
• Remove electrons from the electron shell
of the highest n
• If there is a choice of a subshell within the
nth subshell, the electron electrons are
removed from the maximum l.
E- Configurations of Ions
• Tin
• Tin2+
• Tin4+
Quantum Mechanical Model
of the Atom
Erwin Schrödinger
• Professor of physics!
• Wrote daring equations!
• Confounded his critics!
The quantum mechanical atom
• It is impossible to specify the precise
position of an electron in an atom at a
given instant – Heisenberg Uncertainty
Principle
Quantum Numbers
• Every electron in an atom has a set of four
quantum numbers.
• Pauli Exclusion Principle – No two
electrons in an atom can have the same
set of four quantum numbers.
First Quantum Number (n)
• Principle energy level
• n = 1, 2, 3, 4, etc.
• As n increases, the electron is farther out
from the nucleus.
Second quantum number (l)
• Each principal energy
level includes one or
more sublevels.
• l = the shape of the
orbital (s, p, d, f)
• l : 0 to n-1
Quantum
number l
Type of
sublevel
0
s
1
p
2
d
3
f
Third quantum number ml
• Each sublevel contains one or more
orbitals.
• ml determines the direction in space of the
electron cloud surrounding the nucleus
(orientation of the orbital).
• -l to l
ml = -1
ml = -2
ml = 0
ml = -1
ml = 0
ml = 1
ml = 1
ml = 2
7.6
Fourth quantum number ms
• Associated with electron spin.
• An electron has magnetic properties that
correspond to those of a charged particle
spinning on its axis.
• ms = +1/2 or -1/2
Ex
• For principal quantum level n=5, determine
the number of allowed subshells, and give
the designation of each.
Ex
• Which of the following sets of quantum
numbers are not allowed in the hydrogen
atom?
a. n=2, l =1, ml = -1
b. n=1, l =1, ml = 0
c. n=8, l =7, ml = -6
d. n=1, l =0, ml = 2
Ex
• Give a possible set of values of the four
quantum numbers for all the electrons in a
Boron atom
Ex
• Give a possible set of values of the four
quantum numbers for all the electrons in a
nitrogen atom if each is in the ground state
Ex
• Which of the following electron
configurations correspond to an excited
state? Identify the atoms and write the
ground state electron configuration where
appropriate.
a. 1s22s23p1
b. 1s22s22p6
c. 1s22s22p43s1
d. [Ar]4s23d54p1
E- Configuration Battleship
•
•
•
s-sublevel – Destroyer – 
p-sublevel – Cruiser – 
d-sublevel – Battleship – 