Ionization potentials for single-electron ions

The following table compares the calculated ground-state energies to the experimental values published in the CRC Handbook of Chemistry and Physics.

C: Calculated values from the equation:

$E_{\infty }=\left ( 1-\frac{1}{\gamma } \right )m_{e}c^{2}$

$\gamma =\frac{1}{\sqrt{1-\alpha ^{2}Z^{2}/N_{1}^{2}}}$

(N1=1)

A B C D E F
Z
W
Element Calculated
Bonding
Energy
eV
Ionization
Potential
+Z-1 to +Z
(CRC handbook)
eV
Absolute
Error
(C-D)
eV
Relative
Error
(E/C)
1
1.008
H Hydrogen13.6058713.598440.000030.0000024
2
4.003
He Helium54.4182154.417780.000430.0000079
3
6.941
Li Lithium122.45622122.454290.001930.0000158
4
9.012
Be Beryllium217.72421217.718650.005560.0000255
5
10.811
B Boron340.23832340.225800.012520.0000368
6
12.01
C Carbon490.01750489.993340.024160.0000493
7
14
N Nitrogen667.08823667.046000.042230.0000633
8
16
O Oxygen871.47758871.410100.067480.0000774
9
19
F Fluorine1103.220161103.117600.102560.0000930
10
20
Ne Neon1362.347971362.199500.148470.0001090
11
23
Na Sodium1648.909901648.702000.207900.0001261
12
24.3
Mg Magnesium1962.945711962.665000.280710.0001430
13
27
Al Aluminium2304.511792304.141000.370790.0001609
14
28
Si Silicon2673.658092673.182000.476090.0001781
15
31
P Phosphorus3070.451433069.842000.609430.0001985
16
32
S Sulfur3494.949393494.189200.760190.0002175
17
35.5
Cl Chlorine3947.229713946.296000.933710.0002365
18
40
Ar Argon4427.363634426.229601.134030.0002561
19
39
K Potassium4935.420114934.046001.374110.0002784
20
40
Ca Calcium5471.495425469.864001.631420.0002982
21
45
Sc Scandium6035.682786033.712001.970780.0003265
22
48
Ti Titanium6628.065806625.820002.245800.0003388
23
51
24
52
Cr Chromium7897.829647894.810003.019640.0003823
25
55
Mn Manganese8575.428488571.940003.488480.0004068
26
56
Fe Iron9281.653269277.690003.963260.0004270
27
59
Co Cobalt10016.6314210012.120004.511420.0004504
28
59
Ni Nickel10780.4816110775.400005.081610.0004714
29
64
Cu Copper11573.3493611567.617005.732360.0004953

Whenever physical properties of individual molecules, atoms, or particles are expressed in macroscopic units, (e.g., mass in grams, energy in electron volts, or charge in coulombs), their values are dependent on Avogadro's number.

There are, however, two versions of Avogadro's number used in physics and chemistry. One is mass based (the number of atoms in 12 grams of carbon-12), the other is volume based (the number of particles in 22.414 liters of ideal gas at STP).

The above model relies on the mass based version of Avogadro's number, while experimental values of ionization energy rely on the volume based version.

Ionization energy is measured by heating a gaseous volume of atoms or ions until the spectral emissions attributable to the electron of interest cease.  The total kinetic energy of the gas is determined from its pressure, volume, and temperature.  This total kinetic energy is divided by the number of atoms, calculated from the volumetric version of Avogadro's number.

This close agreement with experimental data suggests that the model might be useful in reconciling the two versions of Avogadro's number.