Download Chapter 6 lecture 2

Electronic Structure of Atoms, Cont’d
The Quantum Mechanical Hydrogen Atom
De Broglie, 1923:
If radiant energy, which is
thought to be a wave, could
behave as a particle
(Einstein), could matter,
which is thought to be a
particle, behave as a wave?
wave-particle duality: could
the electron, in its orbit
about the hydrogen nucleus,
be thought of as a wave with
an associated wavelength?
De Broglie proposes the
existence of a matter
wavelength  for a particle of
mass m and velocity v given
by

h
mv
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given the magnitude of h, when will the matter
wavelength become important?
E.g., calculate the matter wavelength of:
a 50-g golf ball moving at 400 m/s
a Li atom moving at 6.5 x 105 m/s
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The Uncertainty Principle (Heisenberg)
Ascribing wave-like properties to
the electron gives rise to
uncertainties in our ability to
make measurements on the
electron
If we give electron wave-like
properties, then it is no longer
appropriate to imagine the
electron as moving in a welldefined circular orbit
Implications?
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Quantum Mechanics
(Schrödinger, 1926)
Mechanics: branch of physics
which deals with motion
Classical mechanics (Newton):
laws of motion of macroscopic
bodies (planets, tennis balls etc)
Quantum mechanics: laws of
motion of microscopic bodies
Solution of Schrödinger's
equation for H atom leads to
quantum mechanical wave
functions for H atom: orbitals
A quantum mechanical orbital is an allowed
energy state of an electron in a H atom
The square of the orbital represents a probability
of locating the electron in a given energy state
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Bohr model: one quantum number (n)
Quantum mechanical H atom: three quantum
numbers to describe an orbital
principal quantum number, n
restricted to integer
values: n = 1, 2, 3...
larger n: larger orbital,
electron spends more
time farther from
nucleus
note that for the
quantum mechanical H
atom,
1
E  2.18x10 J 
n 
18
n
2
which is the same as the
Bohr result
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azimuthal quantum number, l
restricted to integer values from
0 ... (n-1)
describes shape of orbital
magnetic quantum number, ml
restricted to integer values from - l...0...l
for each l value, there are (2l+1) values of ml
describes orientation of
orbital (i.e., along x, y, z,
etc.)
e.g., what are the allowed values of l for n = 2?
what are the allowed values of ml for this case?
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Electron shells and subshells
shell: orbitals with same value of n
subshell: orbitals with same values of n and l
subshell designations:
l = 0: s
l = 1: p
l = 2: d
l = 3: f
A subshell is designated by a
number (the value of n) and a
letter (corresponding to the value
of l)
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E.g, what is the subshell name
for n=3, l=2? n=2, l=0?
Note that the restrictions on the allowed values of
the quantum numbers give rise to a very
important pattern:
The first shell (n=1) consists of only the 1s
subshell
The second shell (n=2) consists of two subshells
(2s and 2p)
The third shell (n=3) consists of three subshells
(3s, 3p, 3d)
What about the n=4 shell?
Each subshell is further divided into orbitals
each s subshell consists of 1 orbital
each p subshell consists of 3 orbitals
each d subshell consists of 5 orbitals
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Why is this so???
How many orbitals are in an f subshell?
finally, notice in the H atom that orbitals in the
same shell have the same energy....
Why is this???
We construct an orbital diagram for H atom:
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Problems du Jour
For n=5, what are the possible values of l ?
Give the values of n, l, and ml for each orbital in the:
n = 3 shell
4f subshell
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