Secs 7.1-2: Periodic Properties
How is the periodic table organized?
Elements in the same group share the same valence
electron configuration
How does this influence chemical and physical properties
of the elements?
e.g., oxygen and sulfur (group 6A)
These elements share many similar chemical
properties, yet O exists as O2(g) and S as a solid
molecular compound: Why?
What are the similarities between the valence
configurations of O and S?
What is different?
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Development of the Periodic Table
Note that the majority of elements do not exist in
nature in isolated form – they are incorporated into
compounds, and had to be isolated
ca. 1800: 31 elements known
1865: 63 elements known
1869: Mendeleev and Meyer publish similar schemes for
classifying the elements
Both note that similar chemical and physical
properties occur when elements are arranged in order
of increasing atomic weight
Things to keep in mind: at this time, the notion of
the atomic number was unknown, and orbitals
would not be postulated until the late 1920s….
Mendeleev insists that elements with similar
characteristics be lined up in the same families
-leaves blank spaces in the Table
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Mendeleev was able to predict the properties of several
elements very accurately before they were actually found
Now: we want to apply our concept of the quantum
mechanical atom to understand periodic properties of the
elements in terms of electron configurations
Effective nuclear charge
What is the nature of the interaction between an
electron and the nucleus?
The interaction between charges (C) Q1 and Q2 at a
distance d is characterized by Coulomb’s law:
F
kQ1Q2
d2
e.g., in hydrogen, Q1 = +1, and Q2 = -1.
Notice that the force of attraction between an electron and
the nucleus depends on Q1, the size of the nuclear charge,
and the average distance d
Anything that makes Q1 smaller or d larger will decrease
the attractive force between the electron and the nucleus
Implications?
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Pretty easy to understand in a one-e- atom: increase the
distance d between the charges and the attractive force
decreases
What about in a many-electron atom?
Each e- is simultaneously attracted to the nucleus and
repelled by the other e-
Not so easy to think about the interaction between a
single electron and the nucleus
E.g. Li atom: do the 1s and 2s e- experience the
same attraction to the nucleus?
We view the electrostatic interaction between the eand the nucleus in an ‘average’ way in a many-e- atom
Each electron moves in an environment that is an
‘average’ of the electric field created by the nucleus
and all of the other eSo Q1 in Coulomb’s law (the nuclear charge)
changes…
This average electric field (Q1) that is experienced by
an electron in a many-e- atom is called the effective
nuclear charge, Zeff
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How do we calculate Zeff for an electron in a many-e- atom?
This must be done quantum mechanically, but we can get
an decent estimate of Zeff by
Zeff = Z – S
Z = number of protons in the nucleus
S = screening constant
Note that S is the ‘average’ number of electrons between
the e- under consideration and the nucleus
E.g., Li atom: 1s22s1 ground state
For the 2s electron, Zeff = 3-2 = 1
The inner 1s e- ‘screen’ the 2s e- from seeing the
entire nuclear charge of +3
Note that the 2-1s e- are, on average, ~the same distance
from the nucleus – they don’t screen each other
But the 1s electrons are, on average, closer to the nucleus
than the 2s electron, and they can screen the 2s electron
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E.g., calculate Zeff for an n=2 electron in carbon
C: 1s22s22p2 configuration; there are 2 e- ‘between’
an n=2 electron and the nucleus, so
Zeff = 6-2 = 4
Important note: we aren’t as concerned with the actual
value of Zeff as we are with how it changes as we move
around the periodic table
As we move across a period, what happens to Zeff?
We are filling the same subshell (e.g. B- F); e- in
the same subshell don’t screen each other very
well
Zeff = Z-S: Z is increasing, but S is staying the
same
Zeff increases moving across a period!
Note: anything that makes an e- experience increased Zeff
will cause that e- to experience more of an attraction for
the nucleus!
Implications?
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What happens to Zeff as we move down a group on the
periodic table?
Consider the valence electrons of C, Si, and Ge:
C: Zeff = 6 - 2 = 4
Si: Zeff = 14 - 10 = 4
Ge: Zeff = 32 – 28 = 4
Notice that Zeff doesn’t change as much moving down a
group!
But the principal quantum number of the valence shell
does change (e.g. 2p/3p/4p)
implications?
There is a more accurate way to estimate S: Slater’s rules
(p 253 and problem 7.14)
Our simple approximation: each core e- contributes 1.00
to S and each valence electron contributes 0.00 to S.
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Slater’s rules:
e- for which n > n for the electron of interest contributes
0.00 to S
e- with the same value of n as the electron of interest
contribute 0.35 to S.
e- for which n is 1 less than n for the e- under
consideration contribute 0.85, and those with even smaller
n contribute 1.00
E.g. calculate S for a valence electron of fluorine using the
‘simple’ approximation and Slater’s rules
Periodic properties of the elements depend largely upon econfiguration and effective nuclear charge
We want to know how these factors influence:
Atomic and ionic radii
ionization energy
electron affinity
we wish to relate these properties to the way in which
elements undergo chemical changes
In order to do this we must first examine molecules, ions,
and the various types of chemical reactions……..
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Problem du Jour
Arrange the following atoms in order of increasing effective
nuclear charge experienced by the electrons in the n=3 shell:
K, Mg, P, Rh, Ti. Explain the basis for your order.
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