Transcript CHM 111 CHAPTER 7-B Quantum Numbers © 2012 by W. W. Norton & Company.

CHM 111
CHAPTER 7-B
Quantum Numbers
© 2012 by W. W. Norton & Company
Atomic Spectra
•
Blackbody radiation is the visible glow that solid
objects emit when heated.
•
Max Planck (1858–1947): proposed the energy is
only emitted in discrete packets called quanta.
•
The amount of energy depends on the frequency:
E  h 
hc

h  6.626  10 34 J  s
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Atomic Spectra
Albert Einstein (1879–1955):
• Used the idea of
quanta to explain the
photoelectric effect.
•
•
He proposed that
light behaves as a
stream of particles
called photons.
3
Atomic Spectra
4
Atomic Spectra
•
A photon’s energy
must exceed a
minimum threshold
for electrons to be
ejected.
•
Energy of a photon
depends only on
the frequency.
5
Atomic Spectra
•
For red light with a wavelength of about 630 nm,
what is the energy of a single photon and one mole
of photons?
E  h 
hc

h  6.626  10 34 J  s
6
Wave–Particle Duality
•
Louis de Broglie (1892–1987): Suggested waves
can behave as particles and particles can behave
as waves. This is called wave–particle duality.
For Light :  
For a Particle :  
h
mc
h
mv


h
p
h
p
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Quantum Mechanics
•
Niels Bohr (1885–1962): Described atom as
electrons circling around a nucleus and concluded
that electrons have specific energy levels.
•
Erwin Schrödinger (1887–1961): Proposed
quantum mechanical model of atom, which focuses
on wavelike properties of electrons.
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Quantum Mechanics
•
Werner Heisenberg (1901–1976): Showed that it
is impossible to know (or measure) precisely both
the position and velocity (or the momentum) at the
same time.
•
The simple act of “seeing” an electron would
change its energy and therefore its position.
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Quantum Mechanics
h
Heisenberg Uncertainty P rinciple: (x)(m ) 
4
h
Uncertainty in electron's position: (x) 
(4 )(m )
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Quantum Mechanics
•
Erwin Schrödinger (1887–1961): Developed a
compromise which calculates both the energy of an
electron and the probability of finding an electron at
any point in the molecule.
•
This is accomplished by solving the Schrödinger
equation, resulting in the wave function, .
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Quantum Numbers
•
Wave functions describe the behavior of electrons.
•
Each wave function contains three variables called
quantum numbers:
• Principal Quantum Number (n)
• Angular-Momentum Quantum Number (l)
• Magnetic Quantum Number (ml)
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Quantum Numbers
•
Principal Quantum Number (n): Defines the size
and energy level of the orbital. n = 1, 2, 3, 
•
As n increases, the electrons get farther from the
nucleus.
•
As n increases, the electrons’ energy increases.
•
Each value of n is generally called a shell.
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Quantum Numbers
•
Angular-Momentum Quantum Number (l):
Defines the three-dimensional shape of the orbital.
•
For an orbital of principal quantum number n, the
value of l can have an integer value from 0 to n – 1.
•
This gives the subshell notation:
l = 0 = s orbital
l = 1 = p orbital
l = 2 = d orbital
l = 3 = f orbital
l = 4 = g orbital
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Quantum Numbers
•
Magnetic Quantum Number (ml): Defines the
spatial orientation of the orbital.
•
For orbital of angular-momentum quantum number, l,
the value of ml has integer values from –l to +l.
•
This gives a spatial orientation of:
l = 0 giving ml = 0
l = 1 giving ml = –1, 0, +1
l = 2 giving ml = –2, –1, 0, 1, 2,
and so on…...
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Quantum Numbers
•
Spin Quantum Number:
•
The Pauli Exclusion
Principle states that no
two electrons can have
the same four quantum
numbers.
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Quantum Numbers
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