Abstract  single-electron atom electron energy calculation, Bohr in 1913 had resolved to the system of multi-electron atom, is a not resolve global problems. It has not been included in the atomic energy more electronic methods, the answer is yes, in many electronic atomic formula, must understand the electronic check attract potential energy and kinetic energy of electronic relationship between the two in the formula because it is in the "soiled Company" with the other, but also an increase in electronics and electronic the exclusion potential energy, and the other is of secondary importance to the role or negligible. Use this combination formula can be directly calculated the actual atomic or ionic radius, and the ionic radius of ionizing after changes. Of course ion radius than the actual experiment measured the bonding part of larger radius because of the electronic track included here overlap with the energy release.

    Keywords  atomic，radius,，the，electron，energy，calculation,，multi-electron，atom,，can，be，calculated，ionization

1. INTRODUCTION

Since the single-electron problems are solved, people to address the issue more electronic, through the tireless efforts of our predecessors have achieved some results, such as finite element methods, ultra-spherical harmonic function method, perturbation method, variational law. As parameters, algorithms are relatively cumbersome and the subsequent introduction of the computer to deal with, but the results could not be calculated more electronic system response in all major issues, such as the nuclear and electronic attract potential energy, kinetic energy of electronic, electrical and electronic exclusion potential energy, atomic radius, and so on the actual.

Although the original yard of the existence of quantum electronics, fluctuations characteristic, but the yard of the ground state campaign mainly electronic and mechanical compliance with the basic rules of electromagnetic fields.

The atomic structure of many years of exploration, the original preliminary finding out campaign yard electronic form and electronic orbital space structure. So from the simplest two-electron system started, after a period of groping, found that two-electron atom ionization system with a formula can be solved, and then found this expressions For other electronic system is also applicable. Taking into account the size, potential and the distance charge related to the electronic system, and more electronic each other in sports and, in the formula, the introduction of a "charge an average distance", then ionization formula can transform, such formulas can become more concise. After transform the formula, in addition to the calculated electronic check attract potential energy, kinetic energy of electronic, electrical and electronic exclusion potential energy, the ability to calculate the actual atomic or ionic radius. For an atomic system, the electronic track magnetic field interactions, nuclear energy is the kinetic energy of an impact, but the relative electronic potential energy and kinetic energy, electricity, the share of the secondary and that the magnetic field such as electronic orbit interaction with the electron spin magnetic field, limited nuclear energy charge radius, and so on the Gong Xian is negligible and therefore For simplicity's sake-yard unified in one of the amendments said.

2. Theory and Methods

Ionization to the initial establishment of formula relatively simple, but the formula transform a lot of energy, but the process is too occupied two pages, so only provide a paper after the ionization can transform formula:

E = [a (z + z _e) - b-z _e] (z-z _e) + c (1)

Of which:

E for the ionization potential (unit: ev), the nuclear charge number z, z _e for the remaining (ionization) electronics;

_A = e / 8 πε 0 r (2)

(2) the e-electricity for the electronic, ε ₀ for vacuum dielectric constant, r refers to the nuclear ionization electron average distance;

_B = e / 4 πε 0 d (3)

(3) the d-electron ionization refers to the average remaining electronic distance;

C mainly electronic track magnetic potential energy, kinetic energy from nuclear items that, when (z-z _e) larger relativistic effect when it becomes significant.

(1) - show that: multi-electron ionization elements mainly by the energy required to attract potential energy, kinetic energy of a composite (z + z _e) and exclusion potential b × z _e the poor, with the elements of ionizing arising after the net charge (z-z _e) is proportional to the plot.

Which

Composite of a (z + z _e) electronic equivalent of nuclear and attract potential

2 a-z (4)

Less electronic kinetic energy

A (z-z _e) (5)

That is 2 a-z-a (z-z e) ₌ a (z + z _e).

For an atom (or ion) system, the electronic check electronic attract potential energy is the kinetic energy of 2 z / (z-z _e) times, this is a proper element of ionizing can the key to the formula, but also since the settlement of the issue after the single electron has plagued many electronic ground state energy of atoms Operators obstacles.

(1) to (3) of the size of the potential energy, or the point charge and the distance between the average distance, but not the existence of the so-called charge-shielding effect, in order to make consistent with the experimental results and the introduction of shielding coefficient is wrong.

Note: E1 for hydrogen and hydrogen-like ions ionization energy formula, the other analogy; Z for the nuclear charge; Calculated values of less than spectrum value, the error rate was negative, as being contrary; Before the amendment of the positive and negative, and the electronic track combinations, generally before ionization electron orbit coupling a magnetic field, after nuclear energy or ionizing increase, the amendment is the addition of front, contrary to dashes; d: r ionization electronics to electronic remaining distance and the average distance to the nuclear average ratio, the ratio can be used to estimate the electronic position.

Table 1 has been calculated coefficient of three shell ionization energy formula. Use Table 1 He category He and the two-electron ionization ion can be calculated _formula E 2, can be said He, ^{Li +,} Be ^{+ +, B 3 +, C +,} N ^{5 +, O 6 +} ... to the ionizing

Calculated values were: 24.5874,75.6402,153.8966,259.3567,392.0205,551.8879,738.96,… ev,

The experimental data ^were: 24.5874,75.6402,153.8966,259.3752,392.0870,552.0718,739.29,… ev [1];

Use Table 1 Li Li ion type and the three electronic ionization potential formula E ^3, can be said to ^Li, Be +, ^{B +} +, ^{C +,} N ^{+, O} 5 +, F ^{6 +} ... to the ionizing

Calculated values were: 5.3917,18.2112,37.9306,64.5502,98.0697,138.4893,185.809,… ev,

The experimental data were: 5.3917,18.2112,37.9306,64.4939,97.8902,138.1197,185.186,… ev [1].

By contrast we will find that the calculated and experimental data better than meet with other expressions the calculation can also be similar to the results of the ionization potential of these formulas are reasonable, it is atomic, ionic radius of the electronic potential energy, kinetic energy created conditions calculated.

3. The atomic radius, electronic kinetic energy, potential energy calculation

In order to calculate atoms (or ions) radius, electronic kinetic energy, potential energy, the first legislature of their formula:

According to (1) - (5) -, nuclear electronics to be ionizing the average distance (if we use the atomic radius, it is very cumbersome for formulas)

_R ≈ e / 8 πε 0 a (z-z e) (6)

Because of the limited quality of nuclear, nuclear ionizing electronics to the average distance between atoms or ions in general than the actual radius slightly larger than the molecular bonding will have a much greater radius (from orbital overlap and caused by the energy release). When the number of electrons in atoms over 2, the distance between the electronic and nuclear greater than the radius of the electronic track, because when the electron number greater than two, the electronic mutually exclusive, allowing the orbital planes no longer electronic After nucleus;

The electronic and nuclear ionization attract potential

E _absorption ≈ 2 a × z _(z-z e); (7)

The kinetic-energy electron ionization

A _dynamic ≈ E (z-z _e) (z-z _e); (8)

Ionizing electronics and electronic remaining potential exclusion

E _denounced ≈ b × z _e (z-z _e); (9)

The same shell out an electronic per ionizing after narrowing the ionic radius of about doubled (since a similar z-z _e doubled).

Because these formulas do not include nuclear energy, potential energy, and other magnetic track caused the amendment of the c, for a small amount of this error, so use the approximate equation said.

Numerical Calculation of hydrogen atoms

Use (6) to (9) -, and single-electron ionization energy formula E1 coefficient can be calculated electronic ground state atomic hydrogen to nuclear distance

^_R ≈ e / 8 πε 0 × 13.6085 (1-0) = 5.296 × 10 -11 m

(Slightly larger than the hydrogen atom radius ^5.292 × 10 -11 m);

The electronic and atomic nucleus attract potential

E _absorption ≈ 2 × 13.6085 × 1 (1-0) = 27.2170ev;

The kinetic energy of electronic

E _dynamic ≈ 13.6085 (1-0) (1-0) = 13.6085 ev;

Numerical Calculation of helium atom

Use (6) to (9) -, and two-electron ionization energy formula E2 coefficient can be calculated easily helium atom electronic ground state, the average distance to the nuclear

_R ≈ e / 8 πε 0 × 13.6018 (2-1)

⁼ 5.293 × 10 -11 m (slightly less than hydrogen atom);

The electronic and atomic nucleus attract potential

E _absorption ≈ 2 × 13.6018 × 2 (2-1) = 54.4072ev;

The kinetic energy of electronic

E _dynamic ≈ 13.6018 (2-1) (2-1) = 13.6018 ev;

The two electronic potential exclusion

E _denounced ≈ 16.9564 × 1 (2-1) = 16.9564ev;

Ionizing remaining after a narrow radius of the electronic track

^_R ≈ e / 8 πε 0 × 13.6085 (2-0) = 2.648 × 10 -11 m (about narrowing doubled).

That is the ground state of helium atoms first ionization only so it is necessary to 24.5874 ev of energy, it must pay the check electronic attract potential 54.4072 ev, and then minus the electronic kinetic energy 13.6018 ev, two electronic exclusion potential 16.9564 ev, coupled with the amendment of 0.7383.

The amendments contained in the magnetic potential energy, potential energy Although relatively small, but the dual-track electronic s magnetic potential energy, or the ratio p, d, f ... track magnetic structure of the excellent potential to several times, because the two electronic s orbit is close reverse movement.

The hydrogen atoms and helium atoms few make a comparison between the calculated results will be found, their radius almost the same, because the helium-hydrogen nuclear charge number is double, so the helium check electronic check attract potential of hydrogen is the electronic attract potential double. However, the kinetic energy of electronic Why so close? This is the two electronic exclusion helium the result, because the two electronic exclusion helium role to enable electronic with the same speed, the same distance, but also around the nuclear charge twice the amount of hydrogen helium-nuclear movement.

Use (6) to (9) -, together with other ionization coefficients can be calculated formula, the same can be calculated other atoms or ions radius, and their potential energy, kinetic energy, and so on.

The first ionization coefficients formula can determine the size of atomic radius, from Table 1 coefficient of size, can directly see that the atomic radius of the same shell is relatively close, the same cycle is not the first atomic radius than the last atomic radius much larger, such as hydrogen and helium atoms almost the same radius, Ne than the lithium atom radius of only about 4% large.

4. Conclusion

By using a simple formula ionization energy, atomic resolved more electronic, ionic radius of the electronic potential energy, kinetic energy, although very simple formula, but it clearly tells us that atoms or ions, ionization energy needs is that the several major components, as well as checking, the attraction of potential energy and kinetic energy of the electronic mutual relations. To improve accuracy, a need to track the electronic magnetic potential energy (the combination of the track with the electronic mode) and nuclear energy, and so separated, but also to take into account relativistic effects, and of course, this will increase the difficulty of computing. Electronic atomic, ionic radius of the system, the electronic potential energy, kinetic energy of the preliminary settlement, which recognize the true atomic structure, and explore the molecular mechanism of bonding will have a real significance to the settlement of the many-body problem celestial bodies has some reference value.

References

[1] Li M L. Quick Search Data Handbook for Chemistry [M], Beijing: Chemical Industry Press, 2003.12

李梦龙. Chemical data速查Manual [M], Beijing: Chemical Industry Publishing House, 2003.12