Research: Science and Education Ionization Energies of Atoms and Atomic Ions Peter F. Lang and Barry C. Smith* School of Biological and Chemical Sciences, Birkbeck College (University of London), Malet Street, London WC1E 7HX, England; *[email protected] The ionization energy of an atom depends on its atomic and atomic ions. Ionization energies derived from optical and number and electronic configuration. Ionization energies tend mass spectroscopy and calculations ranging from crude ap- to decrease on descending groups in the s and p blocks (with proximations to complex equations based on quantum me- exceptions) and group 3 in the d block of the periodic table. chanical theory are accompanied by assessments of reliability Successive ionization energies increase with increasing charge and a bibliography (2). Martin, Zalubus, and Hagan reviewed on the cation. This paper describes some less familiar aspects energy levels and ionization limits for rare earth elements (3). of ionization energies of atoms and atomic ions. Apparently Handbook of Chemistry and Physics (4) contains authoritative irregular first and second ionization energies of transition data from these and later sources. For example, an experi- metals and rare earth metals are explained in terms of the mental value for the second ionization energy of cesium, electronic configurations of the ground states. A semiquan- 23.157 eV (5), supersedes 25.1 eV (2). titative treatment of pairing, exchange, and orbital energies accounts for discontinuities at half-filled p, d, and f electron Periodicity shells and the resulting zigzag patterns. Third ionization energies of atoms from lithium (Z = We begin with a reminder of the difference between ion- 3) to hafnium (Z = 72) are plotted against atomic number, ization potential and ionization energy. Ionization potential Z, in Figure 1. Values are from reference (4) except those for is the electric potential (measured in volts) required to sepa- Cs (Z = 55) and Ba (Z = 56) from the Journal of the Optical rate an electron from the orbital system in free space with Society of America (5, 6). The first peak occurs at Be2+ (Z = the kinetic energy remaining unchanged. Ionization energy 4), which has the electronic configuration 1s2. Peaks corre- is the work done in removing the electron at zero tempera- sponding to filled s, p, d, f, and half-filled d and f orbitals ture and is measured conveniently in electronvolts, where 1 ᎑ illustrate the shell model of the atom (7). Figure 1 provides eV = 1.6022 × 10 19 J. The molar ionization energy, or change ᎑ a more compelling demonstration of periodicity than plots in molar internal energy, is N eV = 96.485 kJ mol 1 where A of first ionization energy (8) where transition metals and rare N is the Avogadro constant. A earth metals do not show zigzag patterns. Ionization wavenumbers (reciprocal wavelengths) are For M2+ ions, 3d orbitals have lower energies than 4s derived from series limits of atomic spectral lines. The en- ᎑ ᎑ ᎑ orbitals (9), 4d orbitals have lower energies than 5s orbitals, ergy per cm 1 is 1.2398 × 10 4 eV or 1.9864 × 10 23 J. The ᎑ ᎑ and 5p orbitals have lower energies than 4f orbitals. molar energy per cm 1 is 11.962 J mol 1. s Electrons Sources of Data Figure 2 shows how first ionization energies decrease Three volumes containing wavenumbers and atomic en- from hydrogen to cesium and from helium to barium. ergy levels (1) preceded the critical survey by Moore of ion- Straight lines joining ionization energies from five pairs of ization limits from ground state to ground state for atoms group 1 and 2 atoms have intercepts of approximately 2.6 160 140 120 100 Figure 1. Third ionization 80 energies from lithium to hafnium. 60 Ionization Energy / eV 40 20 0 10 20 30 4050 60 70 Atomic Number 938 Journal of Chemical Education • Vol. 80 No. 8 August 2003 • JChemEd.chem.wisc.edu Research: Science and Education eV. The intercept for lithium and beryllium is 1.46 eV but 30 there is no reason to believe that the Moore values are incor- rect. First ionization energies of francium and radium, not shown in Figure 2, are greater than those of cesium and 25 1s barium respectively as a result of poor shielding by 4f elec- trons. 20 First ionization energies of atoms from hydrogen to be- ryllium are plotted in Figure 3. The ionization energy of he- lium is greater than that of hydrogen but less than four times 15 as great (10) because the electrons provide some screening for each other as mutual repulsion pushes them away from the nucleus. The outer electron of lithium occupies a new 10 2s shell screened by two electrons and the ionization energy is Ionization Energy / eV 3s 4s lower than that of hydrogen or helium. Similarly, the first 5s ionization energy of beryllium is higher than that of lithium 5 6s but much lower than that of helium. Second ionization en- ergies from helium to boron are higher and follow a similar 0 pattern. Other points correspond to third, fourth, and fifth 012 ionization energies of the respective atoms. Number of s Electrons Ionization energies of atomic hydrogen and one-electron Figure 2. First ionization energies of group 1 and group 2 atoms. atomic ions, at the left of Figure 3, are approximately pro- portional to the electron–nucleus attraction, Z 2. They are re- produced with reasonable accuracy by the following 400 expression, where RM is the appropriate Rydberg constant and α is the Sommerfeld fine structure constant (11): 350 V 2 2 α RZM 11+ ZZ()− 300 4 250 Screening (electron–electron repulsion) reduces electron– IV nucleus attractions in helium and two-electron atomic ions 200 but ionization energies are not functions of simple squares, (Z − S)2, where S is a screening constant (12). The correct 150 expression takes account of relaxation by the remaining elec- III tron (13): Ionization Energy / eV 100 5Z 5 II Z 2 − + 50 4 16 I 0 The square roots of the first ionization energies plotted HHeLiBeB C N O against atomic number for six isoelectronic series are shown Atom in Figure 4. The one-electron plot falls close to a straight line Figure 3. Energies to remove 1s or 2s electrons from atoms or ions. through the origin. Differences between square roots of suc- Roman numerals denote the ionization number. cessive ionization energies for the other series confirm increas- ing curvature from left to right. Gradients for 2s series approach one half and gradients for 3s series approach one third of the gradient for the one-electron series. Their ion- 25 ization energies are based on quadratic expressions, where n 1s is the principal quantum number of the electron, and b and 20 c are constants characteristic of the series: 2 Z 15 2s − bZ+ c n 3s 10 p Electrons 5 First ionization energies of atoms from the first three Ionization Energy / eV periods of groups 13 to 18 (2p, 3p, and 4p electron series) form zigzag patterns in Figure 5. First and second ionization 0 HHeLiBeB C N O FNeNa Mg Al Si P S Cl energies of atoms from the next two periods (5p and 6p se- Atom ries) appear in Figure 6. Gallium has a slightly higher first ionization energy than aluminum because of relatively poor Figure 4. Square roots of energies to remove 1s, 2s, or 3s electrons. JChemEd.chem.wisc.edu • Vol. 80 No. 8 August 2003 • Journal of Chemical Education 939 Research: Science and Education shielding by 3d electrons. Thallium and lead have higher first tion energy is correct (15). Condon and Shortley identified ionization energies than indium and tin, respectively, because differences between theoretical and experimental values for of poor shielding by 4f electrons. First ionization energies a number of atoms (16) but spin–orbit coupling effects of vary in the order B > Al < Ga > In < Tl and C > Si > Ge > Sn this magnitude were not observed. < Pb but decrease with increasing atomic number down First ionization energies at the bottom of Figure 7 in- groups 15 to 18. Lead and bismuth have greater second ion- crease from boron to nitrogen, decrease to oxygen, and in- ization energies than tin and antimony respectively. crease to neon. Second ionization energies increase from The first ionization energy of bismuth appears to be carbon to oxygen, decrease to fluorine, and increase to so- anomalous. The increase from thallium to lead is followed dium. Third, fourth, and fifth ionization energies of the re- by a decrease to bismuth rather than the expected increase spective atoms show similar patterns. to approximately 8 eV (14). It has been claimed that spin– Discontinuities at half-filled p orbitals are convention- orbit coupling by the Russell–Saunders scheme would lower ally attributed to repulsion between electrons of opposite spin the ground state of Bi+ by 0.8 eV and that the lower ioniza- occupying the same orbital in the second half of a subperiod. 25 25 2p II 3p 5p 20 20 4p 6p 15 15 I 10 10 Ionization Energy / eV Ionization Energy / eV 5 5 0 0 13 14 15 16 17 18 13 14 15 16 17 18 19 Group Group Figure 5. Energies to remove first p electron. Figure 6. Energies to remove first and second p electrons. Roman numerals denote the ionization number. 25 180 ionization energy V modified ionization energy 160 pairing energy 20 exchange energy 140 120 IV 15 100 10 80 III 60 Ionization Energy / eV 5 II Ionization Energy / eV 40 20 I 0 0 BCNOFNeNaMgAlSi -5 Atom BC NOFNe Figure 7. Energies to remove 2p electrons.