Chapter 7Atomic Energies and
Periodicity
Department of Chemistry and Biochemistry
Seton Hall University
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Nuclear Charge
• n - influences orbital energy• Z - nuclear charge also has a
large effect• We can measure this by
ionization energies (IE)– A A + e-
• Consider H and He+
– H H+ + e- 2.18 10-18 J– He He+ + e- 8.72 10-18 J
• Orbital stability increases with Z2
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Electron-electron Repulsion
• Negatively charged electron is attracted to the positively charged nucleus but repelled by negatively charged electrons
• Screening, , is a measure of the extent to which some of the attraction of an electron to the nucleus is cancelled out by the other electrons
• Effective nuclear charge– Zeff = Z -
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Screening
• Complete screening would mean that each electron would experience a charge of +1
• Consider He– w/o screening the IE would be the
same as for He+
– Complete screening the IE would be the same as for H
– Actual IE is between the two values
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Screening
• Screening is incomplete because both electrons occupy an extended region of space, so neither is completely effective at screening the other from the He2+ nucleus
• Compact orbitals (low values of n) are more effective as screening since they are packed tightly around the nucleus
• Therefore, decreases with orbital size (as n increases)
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Screening
• Electrons in orbitals of a given value n screen the electrons in orbitals with larger values of n
• Screening also depends on orbital shape (electron density plots, 2 vs r, help show this)
• Generally, the larger the value of l, the more that orbital is screened by smaller, more compact orbitals
• Quantitative information about this can be obtained from photoelectron spectroscopy
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Structure of the periodic table
• The periodic table is arranged the way it is because the properties of the elements follow periodic trends
• Elements in the same column have similar properties
• Elemental properties change across a row (period)
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Electron configurations
• The Pauli Exclusion Principle– No two electrons can have the
same four quantum numbers
• Hund’s rule– The most stable configuration is
the one with the most unpaired electrons
• The aufbau principle– each successive electron is placed
in the most stable orbital whose quantum numbers are not already assigned to another electron
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Orbital diagrams and rules
• The Pauli Exclusion Principle - no two electrons may have the same four quantum numbers.
• Practically, if two electrons are in the same orbital, they have opposite spins
• Hund’s Rule - when filling a subshell, electrons will avoid entering an orbital that already has an electronic in it until there is no other alternative
• Consider the dorm room analogy (I suggested this to the author!!!)
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Summary of the rules
• Each electron in an atom occupies the most stable orbital available
• No two electrons can have the same four quantum numbers
• The higher the value of n, the less stable the orbital
• For equal values of n, the higher value of l, the less stable the orbital
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Shell designation
• The shell is indicated by the principle quantum number n
• The subshell is indicated by the letter appropriate to the value of l
• The number of electrons in the subshell is indicated by a right superscript
• For example, 4p3
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Electronic configurations
• We use only as many subshells and shells as are needed for the number of electrons
• The number of available subshells depends on the shell that is being filled– n = 1 only has an s subshell– n = 2 has s and p subshells– n = 3 has s, p and d subshells
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Example
• Consider S
• Sulfur has 16 electrons
• Electronic configuration is therefore1s22s22p63s23p4
• d and f subshells are used for heavier elements
• You are expected to do this for any element up to Ar
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Core and valence shells
• Chemically, we find that the electrons in the shell with the highest value of n are the ones involved in chemical reactions
• This shell is termed the valence shell• Electrons in shells with lower n
values are chemically unreactive because they are of such low energy.
• These shells are grouped together as the core
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Electron configurations and the periodic table
• We develop a shorthand for the electron configuration by noting that the core is really the same as the electron configuration for the noble gas that occurs earlier in the periodic table
• E.g. for S (1s22s22p63s23p4), the core is 1s22s22p6 which is the same as the electron configuration for Ne
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Atomic properties
• Ionization energy (IE)A(g) A+
(g) + e-
• Electron affinity (EA)A(g) + e- A-
(g)
• Ion sizes– Cations are smaller than the
neutral atom– Anions are larger that the neutral
atom
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Electron configuration shorthand
• We can then write the electron configuration of S as [Ne]3s23p4
• We note that the valence shell electron configuration has the same pattern for elements in the same group
• For S (a chalcogen) all the elements have the valence electron configuration[core]ns2np4
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Periodic trends
• Atomic radii decrease across a period
• Atomic radii increase down a group
• Ionization energies increase across a period
• Ionization energies decrease down a group
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Near degenerate orbitals
• degenerate orbitals are those that have the same energy
• normally, certain orbitals will be degenerate for quantum mechanical reasons
• near degenerate orbitals have close to the same energy for a variety of reasons
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Ion electronic configurations
• Electronic configurations for ions involves adding or subtracting electrons from the appropriate atomic configuration
• Example: Na Na+
– 1s22s22p63s1 1s22s22p6
• Example: Cl Cl-
– 1s22s22p63s23p5 1s22s22p63s23p6
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Magnetic properties
• The spin of electrons generates a magnetic field
• Two types of magnetism• Diamagnetism - all electrons are
paired• Paramagnetism - one or more
electrons are unpaired• In solids, two types of condensed
phase magnetism results in bulk magnetic properties - ferromagnetism and antiferromagnetism
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Energetics of ionic compounds
• Ions in solids have very strong attractions (ionic bonding)
• Due mostly to cation-anion attraction, and includes a component termed lattice energy
• We can calculate this energy from a Born Haber cycle
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Path yielding a net reaction
• Vaporization Evaporization = 108 kJ/mol
• Ionization E = IE = 495.5 kJ/mol• Bond breakage E = ½(bond energy) = 120
kJ/mol• Ionization E = EA = -348.5 kJ/mol• Condensation - includes all ion-ion attractive
and repulsive interactions (the lattice energy)
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The Born-Haber Cycle
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Calculating the lattice energy
• Coulomb’s law allows us to calculate the electrical force between charged particles
• q1,q2 are the electrical charges of the particles
• k = 1.389 105 kJ pm/mol
• r = interionic distance in pm
r
qqkEcoulomb
))(( 21
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Calculating the lattice energy
• Result of calculation yields a value of -444 kJ/mol
• This includes only part of the lattice energy, since the coulombic interactions do not stop at the individual ions pairs.
• An expansion of Coulomb’s law to include the three dimensional ion interactions yields a value for the lattice energy of -781 kJ/mol
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3 D interaction in crystal
• Note that NaCl extends in all directions
• Each ion experiences attractions and repulsions from other ions past the ones directly in contact
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The overall ionic bonding energy
• The energy for the overall process:Na(s) + ½Cl2 (g) NaCl(s)
• Calculated = -406 kJ/mol
• Actual = -411 kJ/mol
• This treatment assumes the interaction between Na+ and Cl- is only ionic. The slight discrepancy is ascribed to a small degree of electron sharing
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Why not Na2+Cl2-?
• Main reason is the very large ionization energy of the core of NaNa Na+ IE1 = 495.5 kJ/molNa+ Na2+ IE2 = 4562 kJ/mol
• EA2 for Cl is expected to be large and positive
• Basic point is that it costs way too much energy to ionize the core of Na
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Ion stability
• Group 1 and 2 ions will lose all of their valence electrons
• Above Group 2, removal of all valence electrons is generally not observed
• Anions will generally add enough valence electrons to fill the valence shell