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