Lecture 25 Quantum Mechanics of Atoms and Atomic Systems

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Lecture 25Quantum Mechanics of Atoms and Atomic
Systems
Chapter 28.10 ? 28.14
Outline

• Quantum Mechanics and Periodic Table
• Atomic Structure and Conductivity

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Quantum Numbers
Three quantum numbers determine the size and
shape of the probability cloud of an atomic
electron. n ? the principal quantum number
(0,1,2, n) l ? the orbital quantum number
(0,1,2, n ?1) ml ? the magnetic quantum number
(?l, l)
The 4th, spin quantum number (ms) determines the
maximum number of electrons allowed on an
orbit. ms 1/2 or ?1/2
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Energy Level Diagram for Hydrogen
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Electron Shells and Subshells
All states with the same principal quantum number
n form a shell. K-shell corresponds to n1.
States with a given n and l form a
subshell. Subshell s has n 1, l 0 p ? n 2,
l 1
The maximum number of electrons in a subshell is
2(2l1).
Examples shell K (n1) has 1 subshell s (l0)
and the maximum possible number of electrons 2
(ms?1/2). Shell L (n2) has 2 subshells (s and
p, l0,1). Two electrons can be on s and 6 on p ?
total of 8 electrons.
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Problems
Find the radius of the second orbit, ionization
energy from the 2nd orbit, and transition
wavelength between the 2nd and 3rd orbit in a
singly ionized helium atom.
En ? 13.6 Z2/n2 eV
Atom He, Z 2
rn 0.0529 n2/Z nm
Orbits nf 2, ni 3
1/? RH Z2(1/nf2 ? 1/ni2)
Solution
r2 0.0529 22/2 nm 0.1058 nm
E2 13.6 22/22 eV 13.6 eV
1/? 1.097 107 22 (1/22 ? 1/32) nm ? ? 164 nm
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The Exclusion Principle
In 1925 Wolfgang Pauli proposed that No two
electrons in an atom can have the same set of the
four quantum numbers.
This exclusion principle explains the electronic
structure of complex atoms. The more electrons
the atom has, the more levels is
filled. Completely filled shells are called
closed.
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The Periodic Table
Halogens are followed in atomic number by noble
gases, then by alkali metals. This is suggestive
of a periodical law in properties of chemical
elements.
The Periodic Law Elements (listed in order of
atomic number) with similar chemical and physical
properties appear at regular intervals.
The periodic law was first formulated by Dimitri
Mendeleev of Russia in 1869. Predictions unknown
elements Unexpected success noble gases
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Chemical Properties of Elements
Inert (Noble) Gases
Outer shells are closed ? the electrons are
tightly bound to the atom ? chemically passive
Hydrogen and Alkali Metals Single outer
electrons, which see only e charge and are
loosely bound to the nucleus, ? lose the
outermost electrons in chemical reactions, have
similar behavior, and are chemically active
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Chemical Properties of Elements
Halogen Atoms Outer shells lack 1 electron ?
tendency to pick up such an electron through the
strong attraction of the poorly shielded nuclear
charge.
Metals and Nonmetals Metals have 1 or several
electrons outside the closed shells ? combine
chemically by losing these electrons to
nonmetals Nonmetals lack 1 or few electrons in
the outermost shell ? combine by picking up
electrons from metals or by sharing electrons
with other nonmetals
3D Periodic Table
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Energy Bands
Closely spaced atoms become one quantum
system. The electron energy levels of different
atoms form continuous bands, separated by band
gaps. Electrons may have any energy within bands,
but not within band gaps.
Electrons are distributed from the lowest energy
levels up in agreement with the exclusion
principle.
In metals, the highest energy band is partially
full. In insulators, it is completely full.
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Summary
The exclusion principle allows to determine the
maximum possible number of electrons in each
shell and subshell. Quantum mechanics explains
chemical properties of the existing variety of
elements and large atomic systems.