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Quantum mechanics
provides us with an
understanding of atomic
structure and atomic
properties. Lasers are one of
the most important
applications of the quantummechanical properties of
atoms and light.
Chapter Goal: To
understand the structure and
properties of atoms.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Topics today:
•  The Electron’s Spin
•  Multielectron Atoms
•  The Periodic Table of the Elements
•  Excited States and Spectra
•  Lifetimes of Excited States
•  Stimulated Emission and Lasers
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The electron has an inherent magnetic moment and inherent
angular momentum called spin, designated vector-S.
The z-component of this spin angular momentum is
The quantity ms is called the spin quantum number.
The ms = + ½ state, with Sz = + ½ h-bar, is called the spinup state and the ms = –½ state is called the spin-down state.
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Example: For ℓ=2,
m ℓ = -2, -1, 0, +1, +2
correspond to
three different directions
of orbital motion.
A magnetic moment is
associated with the
electron current.
The z-component of the
magnetic moment appears
to be quantized.
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•  Like a compass needle, a magnetic moment interacts
with an external magnetic field depending on its
direction.
•  Low energy when aligned with field, high energy when
anti-aligned
•  The total energy of a hydrogenic electron in an external
magnetic field is approximately:
 
This means that
spectral lines will split
in a magnetic field
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13.6
eV − µ • B
2
n
13.6
= − 2 eV − µz B
n
13.6
= − 2 eV − m µB B
n
E =−
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A neutral atom moving in uniform magnetic
field feels no net force, only a torque
resulting in spin precession.
In an inhomogeneous magnetic field, the
net force is not zero. It proportional to
magnetic moment along the direction of
magnetic field variation.
An atomic beam passing through an
inhomogeneous field is observed to
separate into discrete beams, one per
quantum angular momentum state.
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The currents and magnetism of
electrons in atoms generally cancel out.
The magnetism of an unbalanced
electron should produce an odd number
(2L+1 values of m) of beams.
Observation of an even number of
beams and oddities in spectral splitting
motivated the idea of intrinsic electron
angular momentum and magnetism.
The electron has two magnetic states
and two values of angular momentum.
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•  Spin up
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 
Spin down
Pauli discovered that two complex waves are required to describe a
non-relativistic electron
In a magnetic field, these are linked and describe “spin orientation/
polarization.” Paul Dirac generalized this. A relativistic electron is
described by four coupled complex waves, two more because an
electron can go backwards in time appearing as an antielectron/
positron. That’s eight waves total counting real and imaginary parts.
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•  When analyzing a multielectron atom, each electron is
treated independently of the other electrons.
•  This approach is called the independent particle
approximation, or IPA.
•  This approximation allows the Schrödinger equation for
the atom to be broken into Z separate equations, one for
each electron.
•  A major consequence of the IPA is that each electron can
be described by a wave function having the same four
quantum numbers n, l, m, and ms used to describe the
single electron of hydrogen.
•  A major difference, however, is that the energy of an
electron in a multielectron atom depends on both n and l.
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Notice for example 2p
states are higher that
2s. They are further
out in radius so see a
nuclear charge
partially screened by
1s and 2s electrons.
Note that the scale and
details will depend on
Z!
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In 1925, Pauli hypothesized that no two electrons in a
quantum system can be in the same quantum state.
In other words, no two electrons can have exactly the
same set of quantum numbers n, l, n and ms.
If one electron is present in a state, it excludes all others.
This statement, which is called the Pauli exclusion
principle, turns out to be an extremely profound statement
about the nature of matter.
It applies to all spin ½ kinds of particles (fermions) , but not
to integer spin particles (bosons) like photons.
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Putting electrons on atom
•  Electrons are obey exclusion principle
•  Only one electron per quantum state
unoccupied
occupied
Hydrogen: 1 electron
n=1 states
one quantum state occupied
Helium: 2 electrons
two quantum states occupied
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n=1 states
Other elements: Li has 3 electrons
⎛ n=2 ⎞
⎜
⎟
⎜ =0 ⎟
⎜ m = 0 ⎟
⎜
1⎟
⎜ ms = + ⎟
⎝
2⎠
⎛ n=2 ⎞
⎜
⎟
⎜ =0 ⎟
⎜ m = 0 ⎟
⎜
1⎟
⎜ ms = − ⎟
⎝
2⎠
⎛ n=2 ⎞
⎜
⎟
⎜  =1 ⎟
⎜ m = 0 ⎟
⎜
1⎟
⎜ ms = + ⎟
⎝
2⎠
⎛ n=2 ⎞
⎜
⎟
⎜  =1 ⎟
⎜ m = 0 ⎟
⎜
1⎟
⎜ ms = − ⎟
⎝
2⎠
⎛ n=2 ⎞
⎜
⎟
⎜  =1 ⎟
⎜ m = 1 ⎟
⎜
1⎟
⎜ ms = + ⎟
⎝
2⎠
⎛ n=2 ⎞
⎜
⎟
⎜  =1 ⎟
⎜ m = 1 ⎟
⎜
1⎟
⎜ ms = − ⎟
⎝
2⎠
⎛ n=2 ⎞
⎜
⎟
⎜  =1 ⎟
⎜ m = −1 ⎟
⎜
1⎟
⎜ ms = + ⎟
⎝
2⎠
⎛ n=2 ⎞
⎜
⎟
⎜  =1 ⎟
⎜ m = −1 ⎟
⎜
1⎟
⎜ ms = − ⎟
⎝
2⎠
n=2 states,
8 total, 1 occupied
n=1 states,
2 total, 2 occupied
one spin up, one spin down
⎛ n =1 ⎞ ⎛ n =1 ⎞
⎜
⎟ ⎜
⎟

=
0

=
0
⎜
⎟ ⎜
⎟
⎜ m = 0 ⎟ ⎜ m = 0 ⎟
⎜ Copyright
⎟ ⎜
⎟
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⎝ ms = +1/2⎠ ⎝©m2008
s = −1/2⎠
Atom
Configuration
H
1s1
He
1s2
Li
1s22s1
Be
1s22s2
B
1s22s22p1
Ne
etc
1s shell filled
(n=1 shell filled noble gas)
2s shell filled
1s22s22p6 2p shell filled
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(n=2 shell filled noble gas)
•  Elements are arranged in the periodic table so that atoms
in the same column have ‘similar’ chemical properties.
•  Quantum mechanics explains this by similar ‘outer’
electron configurations.
•  If not for Pauli exclusion principle, all electrons would
be in the 1s state!
H
1s1
Li
2s1
Na
3s1
Be
2s2
Mg
3s2
B
2p1
Al
3p1
C
2p2
Si
3p2
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N
2p3
P
3p3
H
1s1
O
F
2p4 2p5
S
Cl
3p4 3p5
He
1s2
Ne
2p6
Ar
3p6
•  Orbital electron currents and magnetism generally cancel
in multi electron atoms.
•  Spin and its magnetism generally cancels.
•  Unpaired orbital currents explain diamagnetism
•  Unpaired spin magnetism underlies ferromagnetism
•  When the magnetism of a bulk of atoms aligns, the
material is magnetized.
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An atom can jump from one stationary state, of energy E1,
to a higher-energy state E2 by absorbing a photon of
frequency
In terms of the wavelength:
Note that a transition from a state in which the valence
electron has orbital quantum number l1 to another with
orbital quantum number l2 is allowed only if
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QUESTIONS:
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Consider an experiment in which N0 excited atoms are
created at time t = 0. The number of excited atoms
remaining at time t is described by the exponential function
where
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QUESTIONS:
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An extension of simple Schrodinger
theory, Quantum Electrodynamics
(QED) is the theory describing charged
matter fields/particles interacting with
time dependent quantum
electromagnetic fields. It describes the
creation and destruction (emission and
absorption) of light quanta with the
simultaneous evolution of matter wave
states.
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The output beam contains identical photons with special
coherence properties.
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LASER: Light Amplification by
Stimulated Emission of Radiation
Atoms ‘prepared’ in metastable excited states
…waiting for stimulated emission
Called ‘population inversion’
(atoms normally in ground state)
Excited states stimulated to emit photon from a spontaneous
emission.
Two photons out, these stimulate other atoms to emit.
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Ruby Laser
•  Ruby crystal has the atoms which will emit photons
•  Flashtube provides energy to put atoms in excited state.
•  Spontaneous emission creates photon of correct frequency,
amplified by stimulated emission of excited atoms.
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Ruby laser operation
Relaxation to
metastable state
(no photon emission)
3 eV
2 eV
1 eV
Metastable state
PUMP
Transition by stimulated
emission of photon
Ground state
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