16. ON IONIZATION POTENTIALS of ATOMS

 

In the tables of experimental values of potentials of ionization a lot of information on a constitution of atoms is enciphered, but, while, this information will not be utilized rather effectively because of absence of constitutive ideas. Knowledge, which one we have obtained from the previous chapters could clear up this problem (qualitatively, these tables are already clear and in them there is no "by abnormal" numerals), but the business strongly is complicated by that the binding energy of a given electron with a nucleus includes not only electrostatic interaction, but also interaction of a given electron with all other electrons and simultaneously effective magnetic interaction. Besides at removal of an electron there is a reorganization of all electronic structure of atom. At the same structure of electrons, with increase of nuclear charge the eccentricity of orbits of electrons, as we have found out on an example of helium, drops at first sharply, then slowly. It gives in strengthening connection of an electron with a nucleus at the expense more near-circular orbits on the one hand, and to abatement of this connection at the expense of the greater interaction with other electrons, on the other hand. We have an analytical expression only for one of three simultaneously of varying parameters - binding energy of a given electron with a nucleus, which one of the theory of hydrogen-like atoms can be noted so:

                                                                      (16.1),

where: EZ - potential of ionization of a hydrogen-like atom with nuclear charge Z, and EH  - potential of an atomic ionization of hydrogen. Apparently, that here we have that case, when without good mathematical idea to decide a problem about potentials of ionization of atoms it is impossible. And the idea is encompass following (by the way, it has blanket character and can be utilized for a wide range of similar problems). Let's enter into the formula (16.1) concepts of an effective charge:

                       Zeff=AZ                                                (16.2),

where A reflects combined effect of interaction of electrons among themselves and magnetic interaction. Let's substitute (16.2) in (16.1) and is conversed to a view:

                                                         (16.3),

where: EMn - n-th potential of ionization М - similar of atom, EM1 - first potential of ionization of M-similar atom, Z - charge of an ion, which one will be formed at removal of a given electron, A - parameter depending on a constitution of electronic shells of M-similar atom.

The formula (16.3) will be valid, at A=const, only at Z, since the shape of orbits of electrons depends from Z, especially at small Z. More often in the tables give experimental values of the first ten potentials of ionization and even it completely insufficiently to compute a precise parameter value A in the formula (16.3). To decide this problem, we shall describe experimental values of potentials of ionization М-similar of atoms by any empirical expression, but with indispensable by a requirement, that it at Z  gave the formula (16.3). Then it is not required to know a major series of potentials of ionization and parameter A it is possible to compute with any precision for anyone М-similar of atom.

For example, for the first three periods of the table of the Mendeleyev I tender following semiempirical dependence (deduction it is not given, since does not introduce interest, parameter B in this dependence no object):

                              (16.4).

The expression (16.4) at Z gives (16.3), that is an indispensable requirement.

For boron-like of atoms (as an example), in (16.4): А=0.63406, В=0.06633. The matching of experimental values of ionization energy with calculation on (16.4) is given in table 16.1.                                                                                                                                                 Table 16.1.

Element

H

He

Li

Be

B 

A

1.00000

0.74271

0.78910

0.60122   

0.63406

Element

 C

N

O

F

Ne

A

0.54574

0.48029

0.49382

0.43789

0.39704

 Element

Na

Mg

Al

Si

P

A

0.54411

0.45078

0.50804

0.44081

0.39181

Element

S

Cl

Ar

 

 

A

0.39043

0.35119

0.31984

 

 

 

 

 

 

 

 

Boron-like atom

C+1

N+2

O+3

F+4

Ne+5

 

Z

2

3

4

5

6

Е exp. (eV)

24.376

47.426

77.39

114.21

157.9

Е on (57), eV

24.376

47.350

77.25

114.06

157.8

Boron-like atom

Na+6

Mg+7

Al+8

Si+9

 

 

Z

7

8

9

10

 

Е exp. (eV)

208.44

256.84

330.1

401.3

 

Е on (57), eV

208.37

256.83

330.1

401.3

 

Table 16.2.

 The parameter values A for elements of the first three periods are given in table 16.2.

 As the error does not exceed 0.2 %, we shall consider expression (16.4) satisfactory for practical use.

 For all remaining elements the expression (16.4) does not allow any more enough precisely to compute parameter A because completely of other constitution of shells (see tab. 15.1) and other empirical expression is required, which one us now to interest will not be, as the principle is clear.

 Because of that parameter A is liberated from influence of interaction of an electron with a nucleus and its value does not depend on a constitution М-similar

of atom (including from reorganization of electronic structure at removal of a given electron), apparently, that the electrons forms the same shell of atom and which are taking place from its nucleus on same distance should have and identical ionization energy E0:

                                                             (16.5).

 It is clearly, that in the first short period E0=13.595 eV, i.e. is peer to ionization energy of atom of hydrogen. Really, for helium: E0 = EHe1×A2 = 24.58/0.742712 = 13.559 eV, therefore value 24.58 – 13.559 = 11.021 eV is stipulated, in basic, magnetic interaction of two electrons in atom of helium (if not to take into consideration gravidynamic interaction). For elements of the second period E0=3.3535 eV, and third period E0=1.5771 eV. Substituting these values in (16.5), we shall discover the first potentials of ionization of these elements; they are shown in table 16.3.

Element

Li

Be

B

C

N

Е exp. (eV)

5.39

9.32

8.296

11.264

14.54

 Е on (16.5), (eV)

5.39

9.28

8.341

11.259

14.54

Element

O

F

Ne

Na

Mg

Е exp. (eV)

13.614

17.418

21.559

5.138

7.644

Е on (16.5), (eV)

13.752

17.493

21.273

5.327

7.761

Element

Al

Si

P

S

Cl

Е exp. (eV)

5.984

8.149

10.55

10.357

13.01

Е on (16.5), (eV)

6.110

8.116

10.27

10.346

12.79

Element

Ar

 

Е exp. (eV)

15.755

 

 Е on (16.5), (eV)

15.416

 

 Table 16.3

 Structural parameter A completely correlates with that electronic constitution of atoms, which one we have established earlier. As well as it was necessary to expect, the constitution of atom completely determines energy of connections of electrons in its composition. Shell arrangement of electrons around of a nucleus was confirmed. Is shown the essential influence of magnetic interaction to electron-binding energy with atom (in which one is included and gravidynamic interaction, but it in this case is insignificant). The experimental potentials of ionization completely correspond to a constitution of atoms enunciated in this book.

 

16.1. Ion structure

 

On a figure 16.1.1 the relation of an ionization energy of ions of different elements to total of electrons, inherings to an ion is shown. At 10 electrons the electronic configuration of ions corresponds to a neon, and at 18 electrons - argon. Therefore at the subsequent ionization of such ions the sharp increase of an ionization energy is watched, since it is necessary to shatter filled electronic shell of inert gases. The similarity of curves of a fig. 16.1.1 demonstrates a similarity of electronic structure of the applicable ions. Here only it is necessary to add, that though the electronic structures of ions with the same total number of electrons are similar, but electrons are arranged much closer to a nucleus for multicharge ions, that is quite natural.

In a fig. 16.1.2 for the electronic configuration of ions applicable to argon, the ionization energies E are adduced depending on nuclear charge of an ion (curve 1) and same values which have been counted up on the formula  (curve 2). In matching from a dashed straight line it is visible, that with increase of nuclear charge at the same configuration of electrons the ionization energy is proportional to a square of nuclear charge. The more charge of an ion, the more precisely is executed quadratic relation, i.e. the interplay of electrons among themselves in

this case can be fling aside.


To receive a spectral line in optical range, the loss of exuberant energy of an electron, order 5-10 eV is necessary. At the same time, the electron-binding energy in an ion Fe+13 beaming a green line «coronium» in a spectrum of the Sun makes approximately 450 eV. This ion has 13 electrons and their configuration is look-alike to the electronic configuration of aluminum. The eccentricity of orbit of an exited electron is peer to ratio of exuberant energy to bond energy. This eccentricity is approximately peer a considered case 0.015. Orbits with such small eccentricity are near to a ground state (circular orbit) therefore metastable - electrons the much greater time for transition in a ground state is necessary. In similar cases we can watch «forbidden» (in the terms of official physics) spectral lines, if the ion is in very rarefied environment and can not lose exuberant energy at impacts with other particles.

 

16.2. Calculation of ionization potentials

 

Who though once saw spectra of composite atoms, that can sympathize to the astronomers, which one are compelled to be disassembled in thousand spectral lines not only given element, but also in their mixture with other elements, as it is substantially watched in space objects. In outcome before eyes of the explorer there is such bar code in which one practically it is impossible to be disassembled. Let's presume, that we have a set of spectra of all suspected elements existing on investigated object. Then the modern computer equipment can section a spectrum of a complex mixture into spectra of separate elements. But here there is one more severe difficulty: we do not know spectra of multicharge ions. For example, in a corona of the Sun the bright green line of ions Fe+13 (it is watched assigned to a new element «coronium»). And what all spectrum of this ion and similar to it? It cannot be played back in laboratory conditions, and to make idealized calculation, it is necessary, at least to know potentials of ionization of transition Fe+12 Fe+13Fe+14, which one also cannot be defined experimentally. The given chapter will help to leave from this desperate situation and to calculate potentials of ionization of any multicharge ions with a high accuracy.

New physics introduces formation of atomic spectra thus. All electrons of atom are in a ground state and nothing beam. For each electron this condition is strict individually. If atom properly to jolt, the obtained energy is reallocated between all electrons and they will take everyone the personal exited state. At returning in a ground state each electron will beam some serials of spectral lines, number of lines in each serial, basically, is indefinite. Only limit of each serial indicates, that the electron again has taken a ground state. At increase of nuclear charge density of power condition near to a ground state is augmented, therefore spacing interval between spectral lines changes. But as though electron-binding energy with a nucleus was not great, near to a ground state it will beam photons optical and infra-red diapason. On the basis of the set up mechanism of formation of atomic spectra there is a understandable occurrence of spectra, inclusive many thousand of lines.

In chapter 16 the empirical-formula dependences for calculation of potentials of ionization are adduced, but they cannot be recognized satisfactory. In chapter 16.1 (the figure 16.1.1) is shown, that of ions structure with identical number of electrons is look-alike, and on a figure 16.1.2 is shown, what the ionization energy in a degree 1/2 begin with Z+5 and is higher practically linearly depends on nuclear charge (at the same number of electrons). At a charge < Z+5 interplays of electrons among themselves (magnetic and electrostatic) are reduces a potential of ionization, as far as the potential of ionization in each particular case decreases it is impossible to count up, as it is impossible to decide a many-body problem. At rather large nuclear charge the interplay of electrons among themselves practically does not influence interplay with a nucleus, therefore function E(ion)^1/2 ~ Z becomes linear.

Поэтому расчетная формула будет №14: E14=(1,302Z-14,783)2. Мы в эту формулу должны подставить Z=26. В результате получим искомый потенциал ионизации 363,63 эв. Для иона Fe+14 аналогичные расчеты по формуле 12 дадут 460,92 эв.

The author, using the data «the reference Book of the chemist», т.1, 1963, page 325-327 was not too lazy to compound computational equations for all of elements, the data on an ionization energy (eV) which one are accessible. The outcomes are shown in table 16.2.1. In the first column - character of an element, in the second column - nuclear charge of this element, in the third column - formula for calculation of an ionization energy of any ions, which one contain quantity of electrons, equal number of the formula (and only this quantity!), in the subsequent columns matching experimental value of an ionization energy of ions with calculation under the indicated formula is resulted. For example, we shall count up an ionization energy of an ion Fe+12. The nuclear charge iron 26, in the indicated ion is contained 26-12=14 electrons. Therefore this ion attributes to Si-similar atoms (by analogy with hydrogen-like atoms inclusive one electron). Therefore calculated formula will be №14: E14=(1.302Z-14.783)2. We in this formula should substitute Z=26. In outcome we shall receive a required potential of ionization 363.63 eV. For an ion Fe+14 the similar calculations under the formula 12 will give 460.92 eV.

Table 16.2.1.

Symbol of element

Nuclear charge Z

 

Calculated formula

Nuclear charge

Z+4

Z+5

Z+6

 

Z+7

 

Z+8

 

Z+9

 

H

1

E1=(3.688Z)2

Е(experiment)

340.03

489.65

666.47

870.49

1101.71

1360.13

Е(calculation)

340.03

489.65

666.47

870.49

1101.71

1360.13

He

2

E2=(3.701Z-2.441)2

 

Е(experiment)

391.99

551.93

739.11

953.8

1195.4

1464.7

Е(calculation)

390.65

550.65

738.05

952.83

1195

1454.5

Li

3

E3=(1.852Z-3.062)2

 

Е(experiment)

97.86

138.08

185.14

239.1

299.7

367.2

Е(calculation)

98.05

138.16

185.12

238.95

299.64

367.18

Be

4

E4=(1.857Z-4.182)2

 

Е(experiment)

113.87

157.12

207.2

264.2

328

398.6

Е(calculation)

113.93

157.03

207.01

263.9

327.68

398.36

B

5

E5=(1.869Z-6.134)2

 

Е(experiment)

114.21

157.9

208.44

265.84

330.1

401.3

Е(calculation)

114.21

157.65

208.08

265.49

329.89

401.28

C

6

E6=(1.881Z-7.59)2

 

Е(experiment)

126.4

172.4

225.3

285.13

351.8

425.4

Е(calculation)

125.89

171.64

224.46

284.36

351.34

425.39

N

7

E7=(1.881Z-8.918)2

 

Е(experiment)

138.6

186.8

241.8

304

372.8

448.5

Е(calculation)

138.6

186.43

241.34

303.32

372.37

448.51

O

8

E8=(1.891Z-10.806)2

 

Е(experiment)

141.23

190.42

246.41

309.3

378.9

455.3

Е(calculation)

141.28

189.8

245.49

308.32

378.3

455.44

F

9

E9=(1.905Z-12.404)2

 

Е(experiment)

153.8

205.1

263.3

328.4

400.3

479

Е(calculation)

152.79

203.52

261.5

326.74

399.24

479

Ne

10

E10=(1.915Z-13.94)2

 

Е(experiment)

166.73

220.41

280.99

348.5

422.6

503.8

Е(calculation)

165.64

218.6

378.89

346.52

421.48

503.78

Na

11

E11=(1.303Z-11.524)2

 

Е(experiment)

65.01

88

114.2

143.4

176

211.3

Е(calculation)

64.34

86.94

112.93

142.32

175.11

211.29

Mg

12

E12=(1.296Z-12.227)2

 

Е(experiment)

72.5

96.6

123.9

154.3

187.9

224.9

Е(calculation)

72.4

96.14

123.23

153.69

187.5

224.67

Al

13

E13=(1.293Z-13.719)2

 

Е(experiment)

67.8

91.3

117.9

143.3

180.2

216.9

Е(calculation)

68.26

91.3

117.68

147.4

180.47

216.88

Si

14

E14=(1.302Z-14.783)2

 

Е(experiment)

75

99.4

127.9

159.2

193.1

230.2

Е(calculation)

74,87

99.1

126.72

157.73

192.13

229.92

P

15

E15=(1.319Z-15.977)2 

 

Е(experiment)

82.6

109

139

172

206

246

Е(calculation)

82.52

108.22

137.4

170.07

206.21

245.83

S

16

E16=(1.311Z-16.995)2

 

Е(experiment)

84

111

141

174

209

249

Е(calculation)

85.1

111

140.35

173.13

209.35

249

Cl

17

E17=(1.321Z-18.16)2

 

Е(experiment)

91.8

119

151

185

221

262

Е(calculation)

91.8

118.85

149.4

183.44

220.97

261.99

Ar

18

E18=(1.33Z-19.27)2

 

Е(experiment)

99.8

128.9

161.1

196.4

234.4

276.9

Е(calculation)

99.8

128.14

160.02

195.44

234.4

276.89

K

19

E19=(1.362Z-23.176)2

 

Е(experiment)

65.2

90.6

120

151

185.9

224

Е(calculation)

66.42

90.48

118.24

149.72

184.91

223.8

Ca

20

E20=(1.381-24.525)2

 

Е(experiment)

73

100

130

163

200

241

Е(calculation)

74.29

100

129.53

162.87

200.02

240.99

Sc

21

E21=(1.4Z-26.272)2

 

Е(experiment)

76

103

133

168

206

247

Е(calculation)

76.18

102.58

132.89

167.13

205.29

247.37

Ti

22

E22=(1.515Z-30.497)2

 

Е(experiment)

79

109

143

182

224

271

Е(calculation)

79.08

108.33

142.16

180.58

223.59

271.19

V

23

E23=(1.542Z-32.601)2

 

Е(experiment)

82

113

148

188

231

280

Е(calculation)

81.59

111.83

146.82

186.57

231.07

280.33

Cr

24

E24=(1.528Z-33.879)2

 

Е(experiment)

79

109

144

183

226

274

Е(calculation)

79.3

108.85

143.06

181.95

225.51

273.74

Mn

25

E25=(1.529Z-35.193)2

 

Е(experiment)

83

114

149

189

234

282

Е(calculation)

83.69

114

148.99

188.65

232.99

282

Fe

26

E26=(1.549Z-37.156)2

 

Е(experiment)

86

118

155

196

241

291

Е(calculation)

86.75

118

154.06

194.91

240.56

291

Co

27

E27=(1.557Z-38.75)2

 

Е(experiment)

90

123

160

202

248

300

Е(calculation)

90.57

122.63

159.54

201.3

247.9

299.36

Ni

28

E28=(1.338Z-32.854)2

 

Е(experiment)

93.4

127.5

155

193

234

277

Е(calculation)

99.24

127.69

159.72

195.33

234.52

277.29

Cu

29

E29=(1.061Z-27)2

 

Е(experiment)

62.9

82.1

103

126

150

177

Е(calculation)

64.21

82.34

102.72

125.35

150.23

177.37

Zn

30

E30=(1.102Z-29.148)2

 

Е(experiment)

68.3

88.6

111

136

162

191

Е(calculation)

69.22

88.77

110.75

135.16

162

191.27

Ga

31

E31=(1.073Z-29.767)2

 

Е(experiment)

59.7

78.5

99.2

122.3

146.2

173

Е(calculation)

60.65

78.52

98.68

121.15

145.93

173

Ge

32

E32=(1.119Z-32.233)2

 

Е(experiment)

64.7

84.4

106

129

154

186

Е(calculation)

64.82

84.09

105.86

130.14

156.93

186.21

As

33

E33=(1.053Z-30.298)2

 

Е(experiment)

71

90.8

116

139

165

194

Е(calculation)

75.05

94.4

115.97

139.76

165.77

193.99

Se

34

E34=(1.08Z-32.476)2

 

Е(experiment)

71.6

93

116

141

167

195

Е(calculation)

73.34

93.01

115

139.33

166

195

Br

35

E35=(1.19Z-37.663)2

 

Е(experiment)

77

99.4

124

153

183

216

Е(calculation)

76.51

98.74

123.81

151.71

182.44

216

Kr

36

E36=(1.123Z-35.535)2

 

Е(experiment)

82.3

110.4

131

161

192

225

Е(calculation)

88.08

110.42

135.28

162.66

192.57

225

Rb

37

E37=(1.252Z-44.25)2

 

Е(experiment)

50

67

94

119

147

178

Е(calculation)

50.15

69.45

91.89

117.46

146.17

178

Sr

38

E38=(1.239Z-44.558)2 

 

Е(experiment)

61.2

76

100

126

155

187

Е(calculation)

55.95

76.02

99.16

125.37

154.65

187.01

Y

39

E39=(1.238Z-45.46)2

 

Е(experiment)

59

81

105

132

162

195

Е(calculation)

60.43

81.22

105.06

131.97

161.95

194.99

Zr

40

E40=(1.263Z-47.604)2

 

Е(experiment)

63

85

111

139

170

204

Е(calculation)

63.49

85.21

110.12

138.23

169.52

204

Nb

41

E41=(1.277Z-49.256)2

 

Е(experiment)

67

90

116

146

178

213

Е(calculation)

67.39

89.98

115.84

144.96

177.34

212.98

Mo

42

E42=(1.28Z-50.754)2

 

Е(experiment)

66

89

115

144

176

211

Е(calculation)

66.03

88.47

114.19

143.18

175.46

211

Tc

43

E43=(1.293Z-52.404)2

 

Е(experiment)

70

94

121

151

184

220

Е(calculation)

70

93.32

119.97

149.96

183.3

219.99

Ru

44

E44=(1.308Z-54.191)2

 

Е(experiment)

73

98

126

157

192

229

Е(calculation)

73.84

98.03

125.64

156.67

191.13

229.01

Rh

45

E45=(1.335Z-56.663)2

 

Е(experiment)

77

103

132

164

200

238

Е(calculation)

76.6

101.75

130.46

162.74

198.58

237.99

Pd

46

E46=(1.273Z-54.015)2

 

Е(experiment)

91

119

149

182

218

256

Е(calculation)

92.83

116.98

148.38

181.01

216.88

256

Ag

47

E47=(1.065Z-46.328)2

 

Е(experiment)

63.8

83

104

126

150

158

Е(calculation)

63.79

81.94

102.35

125.04

150

177.21

Cd

48

E48=(0.944Z-40.963)2

 

Е(experiment)

66

83

102

122

144

165

Е(calculation)

66.02

82.25

100.26

120.06

141.63

164.99

In

49

E49=(0.938Z-41.289)2

 

Е(experiment)

71

89

108

127

151

172

Е(calculation)

70.98

87.67

106.11

126.31

148.28

172

Sn

50

E50=(1.023Z-47.629)2

 

Е(experiment)

57

74

93

114

137

162

Е(calculation)

57.96

74.58

93.3

114.1

137.01

162

Sb

51

E51=(1.041Z-49.383)2

 

Е(experiment)

62

80

100

122

146

171

Е(calculation)

61.97

79.44

99.08

120.89

144.86

171.01

Te

52

E52=(1.056Z-51.263)2

 

Е(experiment)

62

80

100

122

147

173

Е(calculation)

61.98

79.73

99.7

121.9

146.34

173

J

53

E53=(1.066Z-52.638)2

 

Е(experiment)

66

85

106

129

154

181

Е(calculation)

66

84.46

105.18

128.19

153.46

181.01

Xe

54

E54=(1.06Z-53.105)2

 

Е(experiment)

70

89

111

135

161

187

Е(calculation)

70.14

89.02

110.14

133.52

159.14

187.01

 NO DATA

Е(experiment)

 

 

 

 

 

 

Е(calculation)

 

 

 

 

 

 

Tu

69

E69=(1.075Z-71.767)2

 

Е(experiment)

45

61

79

99

121

146

Е(calculation)

45

60.57

78.46

98.66

121.18

146

Yb

70

E70=(1.088Z-73.583)2

 

Е(experiment)

48

65

89

104

127

153

Е(calculation)

48.01

64.27

82.9

103.9

127.26

152.99

Lu

71

E71=(1.091Z-74.671)2

 

Е(experiment)

51

68

88

109

133

159

Е(calculation)

51.18

67.98

87.16

108.72

132.66

158.99

Hf

72

E72=(1.1Z-76.216)2

 

Е(experiment)

54

72

92

114

139

166

Е(calculation)

54.52

71.98

91.85

114.15

138.86

166

Ta

73

E73=(1.123Z-78.933)2

 

Е(experiment)

57

75

96

120

145

173

Е(calculation)

56.82

75.01

95.73

118.96

144.72

173

W

74

E74=(1.126Z-80.458)2

 

Е(experiment)

55

73

94

117

142

169

Е(calculation)

54.32

72.18

92.58

115.52

140.99

169

Re

75

E75=(1.123Z-81.066)2

 

Е(experiment)

58

77

98

112?

148

176

Е(calculation)

58.54

76.98

97.95

121.44

147.45

175.99

Os

76

E76=(1.144Z-83.712)2

 

Е(experiment)

61

81

103

127

154

183

Е(calculation)

60.96

80.14

101.93

126.34

153.36

183.01

Ir

77

E77=(1.157Z-85.718)2

 

Е(experiment)

64

84

107

132

160

190

Е(calculation)

63.98

83.83

106.36

131.56

159.44

190

Pt

78

E78=(1.137Z-84.883)2

 

Е(experiment)

69.7

94.4

112

138

166

197

Е(calculation)

69.74

90.02

112.89

138.34

166.38

197.01

Au

79

E79=(Z-75.51)2

 

Е(experiment)

56

73

91

111

133

156

Е(calculation)

56.1

72.08

90.06

110.04

132.02

156

Hg

80

E80=(0.999Z-76.105)2

 

Е(experiment)

61

78

97

117

140

164

Е(calculation)

61.01

77.62

96.22

116.81

139.4

163.99

Tl

81

E81=(0.98Z-76.158)2

 

Е(experiment)

51

67

84

103

123

145

Е(calculation)

51.01

65.97

82.85

101.65

122.37

145.01

Pb

82

E82=(0.996Z-78.226)2

 

Е(experiment)

55

71

89

109

130

154

Е(calculation)

55.2

71

88.77

108.53

130.28

154.01

Bi

83

E83=(1.01Z-80.192)2

 

Е(experiment)

59

76

95

115

138

162

Е(calculation)

58.95

75.48

94.05

114.66

137.31

162

Po

84

E84=(1.01Z-81.215)2

 

Е(experiment)

59

76

94

115

137

?

Е(calculation)

58.75

75.26

93.8

114.38

137.01

?

 

 

16.3 Values of coefficients in the formulas of an ionization energy

 

Values of coefficients in the formulas of an ionization energy of a kind EZ=(AZ-B)2 of chapter 16.2.

On a figure 16.3.1 the course of change of a factor A is shown depending on nuclear charge, and on a figure 16.3.2 - similar course of change of a factor B. As the factor B, on the average, is proportional to nuclear charge, on a figure 16.3.2 the broken line of direct ratio is conducted. From table 16.3.1 and graphs the correlation of factors A and B with degree of fullness of electronic envelopes and subenvelopes of table 15.1 of chapter 15 is legiblly visible and it proves the new form of the table of the Mendeleyev.

Z at E numerically is equal to number of the formula of chapter 16.2, which one is peer to nuclear charge of this element (Z brackets) minus a charge of any ion of this element. Z

A

B

Z

A

B

Z

A

B

Comment

1

3,688

0,000

25

1,529

35,193

49

0,938

41,289

In brackets the number of electrons in a envelope or sub envelope of table 15.1 is indicated

2

3,701    (2)

2,441

26

1,549

37,156

50

1,023

47,629

3

1,852

3,062

27

1,557

38,750

51

1,041

49,383

4

1,857

4,182

28

1,338   (8)

32,854

52

1,056

51,263

5

1,869

6,134

29

1,061

27,000

53

1,066

52,638

 

6

1,881

7,590

30

1,102   (2)

29,148

54

1,060   (6)

53,105

For elements with z=55 up to z=68 there are no data

7

1,881

8,918

31

1,073

29,767

69

1,070

71,767

8

1,891

10,806

32

1,119

32,233

70

1,088

73,583

 

9

1,905

12,404

33

1,053

30,298

71

1,091   (16)

74,871

 

10

1,915    (8)

13,940

34

1,080

32,476

72

1,100

76,216

 

11

1,303

11,524

35

1,190

37,663

73

1,123

78,933

 

12

1,296

12,227

36

1,123   (6)

35,535

74

1,126

80,458

 

13

1,293

13,719

37

1,252

44,250

75

1,123

81,066

 

14

1,302

14,783

38

1,239    (2)

44,558

76

1,144

83,712

 

15

1,319

15,977

39

1,238

45,460

77

1,157

85,718

 

16

1,311

16,995

40

1,263

47,604

78

1,137

84,883

 

17

1,321

18,160

41

1,277

49,256

79

1,000   (8)

75,510

 

18

1,330   (8)

19,270

42

1,280

50,754

80

0,999

76,105

 

19

1,362

23,176

43

1,293

52,404

81

0,980   (2)

76,158

 

20

1,381   (2)

24,525

44

1,308

54,191

82

0,996

78,226

 

21

1,400

26,272

45

1,335

56,663

83

1,010

80,192

 

22

1,515

30,497

46

1,273   (8)

54,015

84

1,010

81,215

 

23

1,542

32,601

47

1,065

46,328

 

 

 

 

24

1,528

33,879

48

0,944   (2)

40,963