Alright class we are going back to quantum numbers.

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Alright class we are going back to quantum
numbers.

• I decided this would be a better lead into dipole
  then just throwing you into the mess.

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Do you remember Wave and Frequency?

• Do you remember plank. Well he is back it is time
  to work on his constant and what it means.
• Also the electromagnetic spectrum.

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Properties of Waves
Wavelength (l) is the distance between identical
points on successive waves.
Amplitude is the vertical distance from the
midline of a wave to the peak or trough.
Frequency (n) is the number of waves that pass
through a particular point in 1 second (Hz 1
cycle/s).
The speed (u) of the wave l x n
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Maxwell (1873), proposed that visible light
consists of electromagnetic waves.
Electromagnetic radiation is the emission and
transmission of energy in the form of
electromagnetic waves.
Speed of light (c) in vacuum 3.00 x 108 m/s
All electromagnetic radiation l x n c
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A photon has a frequency of 6.0 x 104 Hz. Convert
this frequency into wavelength (nm). Does this
frequency fall in the visible region?
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• The wavelength of the green light from a traffic
  signal is centered at 522 nm. What is the
  frequency of this radiation?

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Problem 1

• What is the wavelength (in meters) of an
  electromagnetic wave whose frequency is 3.64 x
  107 Hz?

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Mystery 1, Heated Solids ProblemSolved by
Planck in 1900
When solids are heated, they emit electromagnetic
radiation over a wide range of wavelengths.
Radiant energy emitted by an object at a certain
temperature depends on its wavelength.
Energy (light) is emitted or absorbed in discrete
units (quantum).
E h x n Plancks constant (h) h 6.63 x 10-34
Js
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Calculate the energy (in joules) of a photons
with a wavelength of 5.00 x 104 nm (infrared
region).
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Calculate the energy (in joules) of a photons
with a wavelength of 5.00 x 10-2 nm (x-ray
region).
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Problem 2

• The energy of a photon is 5.87 x 10-20 J. What
  is its wavelength in nanometers?

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Mystery 2, Photoelectric EffectSolved by
Einstein in 1905
hn

• Light has both
• wave nature
• particle nature

KE e-
Photon is a particle of light
hn KE W
KE hn - W
where W is the work function and depends how
strongly electrons are held in the metal
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When copper is bombarded with high-energy
electrons, X rays are emitted. Calculate the
energy (in joules) associated with the photons if
the wavelength of the X rays is 0.154 nm.
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The work function of cesium metal is 3.42 x 10-19
J. Calculate the minimum frequency of light
necessary to eject electrons from the metal.
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The work function of cesium metal is 3.42 x 10-19
J. Calculate the kinetic energy of the ejected
electron if light of frequency 1.00 x 1015 s-1 is
used for irradiating the metal.
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Problem 3

• The work function of titanium metal is 6.93 x
  10-19 J. Calculate the energy of the ejected
  electrons if light of frequency 2.50 x 1015 s-1
  is used to irradiate the metal.
• KE _____x 10-19 J

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Mystery 3, Emission Spectra
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Bohrs Model of the Atom (1913)

1. e- can only have specific (quantized) energy
   values
2. light is emitted as e- moves from one energy
   level to a lower energy level

n (principal quantum number) 1,2,3,
RH (Rydberg constant) 2.18 x 10-18J
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Ephoton DE Ef - Ei
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Calculate the wavelength (in nm) of a photon
emitted by a hydrogen atom when its electron
drops from the n 5 state to the n 3 state.
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Problem 4

• What is the wavelength (in nm) of a photon
  emitted during a transition from ni6 to nf4 in
  the H atom?
• ? _____x 103 nm

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Why is e- energy quantized?
De Broglie (1924) reasoned that e- is both
particle and wave.
u velocity of e-
m mass of e-
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What is the de Broglie wavelength (in nm)
associated with a 2.5 g Ping-Pong ball traveling
at 15.6 m/s?
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Calculate the wavelength of the particle in
each of the following two cases (a) The fastest
serve ever recorded in tennis was about 150 miles
per hour, or 68 m/s. Calculate the wavelength
associated with a 6.0 x 10-2 kg tennis ball
travelling at this speed.
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Calculate the wavelength of the particle in
each of the following two cases (b) Calculate
the wavelength associated with an electron
(9.1094 x 10-31kg) travelling at this speed.
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Problem 5

• Calculate the wavelength (in nm) of a H atom
  (mass 1.674 x 10-27 kg) moving at 7.00 x 102
  cm/s.

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Chemistry in Action Laser The Splendid Light
Light Amplification by Stimulated Emission of
Radiation
Laser light is (1) intense, (2) monoenergetic,
and (3) coherent
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Chemistry in Action Electron Microscopy
le 0.004 nm
STM image of iron atoms on copper surface
Electron micrograph of a normal red blood cell
and a sickled red blood cell from the same person
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Shortcomings of Bohrs model

• Did not account for the emission spectra of atoms
  containing more than on electron.
• Did not explain extra lines in the emission
  spectra for hydrogen when magnetic field is
  applied.
• Conflict with discovery of wavelike properties
  how can you define the location of a wave?

Heisenberg Uncertainty Principle It is impossible
to know simultaneously both the momentum p
(defined as mass times velocity) and the position
of a particle with certainty.
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Schrodinger Wave Equation
In 1926 Schrodinger wrote an equation that
described both the particle and wave nature of
the e-
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Schrodinger Wave Equation

• Wave function (y) describes
• . energy of e- with a given y
• . probability of finding e- in a volume of space
• Schrodingers equation can only be solved exactly
  for the hydrogen atom. Must approximate its
  solution for multi-electron systems.

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Schrodinger Wave Equation
y is a function of four numbers called
quantum numbers (n, l, ml, ms)
principal quantum number n
n 1, 2, 3, 4, .
distance of e- from the nucleus
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Schrodinger Wave Equation
quantum numbers (n, l, ml, ms)
angular momentum quantum number l
for a given value of n, l 0, 1, 2, 3, n-1
l 0 s orbital l 1 p orbital l 2
d orbital l 3 f orbital
n 1, l 0 n 2, l 0 or 1 n 3, l 0, 1,
or 2
Shape of the volume of space that the e-
occupies
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l 0 (s orbitals)
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l 2 (d orbitals)
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Schrodinger Wave Equation
quantum numbers (n, l, ml, ms)
magnetic quantum number ml
for a given value of l ml -l, ., 0, . l
if l 1 (p orbital), ml -1, 0, or 1 if l 2
(d orbital), ml -2, -1, 0, 1, or 2
orientation of the orbital in space
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3 orientations is space
ml -1, 0, or 1
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ml -2, -1, 0, 1, or 2
5 orientations is space
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Schrodinger Wave Equation
(n, l, ml, ms)
spin quantum number ms
ms ½ or -½
ms -½
ms ½
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Schrodinger Wave Equation
quantum numbers (n, l, ml, ms)
Existence (and energy) of electron in atom is
described by its unique wave function y.
Pauli exclusion principle - no two electrons in
an atom can have the same four quantum numbers.
Each seat is uniquely identified (E, R12,
S8) Each seat can hold only one individual at a
time
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Schrodinger Wave Equation
quantum numbers (n, l, ml, ms)
Shell electrons with the same value of n
Subshell electrons with the same values of n
and l
Orbital electrons with the same values of n, l,
and ml
How many electrons can an orbital hold?
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How many 2p orbitals are there in an atom?
How many electrons can be placed in the 3d
subshell?
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List the values of n, l, and ml for orbitals in
the 4d subshell.
What is the total number of orbitals associated
with the principle quantum number n3?
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Problem 6

• Give the values of the quantum numbers associated
  with the orbitals in the 3p subshell.
• n ____
• l ____
• ml____

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Problem 7

• What is the total number of orbitals associated
  with the principle quantum number n4.

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Energy of orbitals in a single electron atom
Energy only depends on principal quantum number n
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Energy of orbitals in a multi-electron atom
Energy depends on n and l
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Fill up electrons in lowest energy orbitals
(Aufbau principle)
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The most stable arrangement of electrons in
subshells is the one with the greatest number of
parallel spins (Hunds rule).
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Order of orbitals (filling) in multi-electron atom
1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt
5p lt 6s
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Write the four quantum numbers for an electron in
a 3p orbital.
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Problem 8

• Write the four quantum numbers for an electron in
  a 4d orbital.

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Electron configuration is how the electrons are
distributed among the various atomic orbitals in
an atom.
1s1
Orbital diagram
H
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What is the electron configuration of Mg?
What are the possible quantum numbers for the
last (outermost) electron in Cl?
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What is the maximum number of electrons that can
be present in the principle level for which n3?
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Problem 9

• Calculate the total number of electrons that can
  be present in the principle level for which n4

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An oxygen atom has a total of eight electrons.
Write the four quantum numbers for each of the
electrons in the ground state..
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Problem 10

• Write a complete set of quantum numbers for each
  of the electrons in boron.

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Paramagnetic
Diamagnetic
unpaired electrons
all electrons paired
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Outermost subshell being filled with electrons
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Write the ground state electron configuration for
sulfur
Write the ground state electron configuration for
palladium which is diamagnetic
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Problem 11

• Write the ground state configuration for
  phosphorus.

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