Chapter 7 Atomic Energies and Periodicity Department of Chemistry and Biochemistry Seton Hall University

2 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  J –He  He + + e  J Orbital stability increases with Z 2

3 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 –Z eff = Z - 

4 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

5 Screening Screening is incomplete because both electrons occupy an extended region of space, so neither is completely effective at screening the other from the He 2+ 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)

6 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

7 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)

8 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

9 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!!!)

10 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

11 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, 4p 3

12 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

13 Example Consider S Sulfur has 16 electrons Electronic configuration is therefore 1s 2 2s 2 2p 6 3s 2 3p 4 d and f subshells are used for heavier elements You are expected to do this for any element up to Ar

14 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

15 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 (1s 2 2s 2 2p 6 3s 2 3p 4 ), the core is 1s 2 2s 2 2p 6 which is the same as the electron configuration for Ne

16 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

17 Electron configuration shorthand We can then write the electron configuration of S as [Ne]3s 2 3p 4 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]ns 2 np 4

18 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

19 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

20 Ion electronic configurations Electronic configurations for ions involves adding or subtracting electrons from the appropriate atomic configuration Example: Na  Na + –1s 2 2s 2 2p 6 3s 1  1s 2 2s 2 2p 6 Example: Cl  Cl - –1s 2 2s 2 2p 6 3s 2 3p 5  1s 2 2s 2 2p 6 3s 2 3p 6

21 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

22 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

23 Path yielding a net reaction Vaporization  E vaporization = 108 kJ/mol Ionization  E = IE = kJ/mol Bond breakage  E = ½(bond energy) = 120 kJ/mol Ionization  E = EA = kJ/mol Condensation - includes all ion-ion attractive and repulsive interactions (the lattice energy)

24 The Born-Haber Cycle

25 Calculating the lattice energy Coulomb’s law allows us to calculate the electrical force between charged particles q 1,q 2 are the electrical charges of the particles k =  10 5 kJ pm/mol r = interionic distance in pm

26 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

27 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

28 The overall ionic bonding energy The energy for the overall process: Na (s) + ½Cl 2 (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

29 Why not Na 2+ Cl 2- ? Main reason is the very large ionization energy of the core of Na Na  Na + IE 1 = kJ/mol Na +  Na 2+ IE 2 = 4562 kJ/mol EA 2 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

30 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