# Ionization energy

The ionization energy (also ionization energy , ionization potential , ionization enthalpy ) is the energy that is required to ionize an atom or molecule in the gas phase , i.e. i.e., to separate an electron from an atom or molecule. It can be delivered by radiation , a high temperature of the material or chemically. In atomic physics , the ionization energy is also referred to as binding energy .

## General

After ionization, a previously electrically neutral atom or molecule has a positive electrical charge . The previously balanced charge difference between the atomic nucleus (s) and the electron shell is shifted by the removal of an electron. One speaks of a positively ionized atom or molecule or a cation . This is indicated by a superscript '+' sign; z. B. a sodium cation is identified as Na + (Na is the element symbol for sodium).

As long as a cation still has electrons, it can be further ionized by adding more energy, but the required energy increases with each additional ionization. In general, the nth ionization energy is the energy required to remove the nth electron. A multiply ionized cation is symbolically identified by a number placed in front of the '+' sign; z. B. a triple ionized aluminum cation is referred to as Al 3+ .

## unit

For a single electron, the ionization energy is given in eV / atom, but for 1  mol of substance in kJ / mol. The conversion factor results from the conversion between eV and J, ie the elementary charge e ; the factor 1000, since kJ is used instead of J; as well as the Avogadro constant for conversion into moles. This results in just one thousandth of the Faraday constant , which is an exact constant expressed in SI units since the revision of the SI in 2019 : ${\ displaystyle N _ {\ mathrm {A}}}$ ${\ displaystyle F = N _ {\ mathrm {A}} \ cdot e}$ 1 eV / atom = 96.485 332 123 310 018 4  kJ / mol,

where on the left the “per atom” is mostly left out.

## First ionization energy and periodic table

The first ionization depends on the attraction force from between the nucleus and the electron to be removed, which according to the Coulomb's formula is calculated:

${\ displaystyle F = k _ {\ mathrm {C}} \ cdot {\ frac {Ze \ cdot (-e)} {r ^ {2}}}}$ With

• Atomic or atomic number${\ displaystyle Z}$ • Elemental charge ${\ displaystyle e}$ • Distance of the electron from the nucleus${\ displaystyle r}$ • Coulomb's constant ${\ displaystyle k _ {\ mathrm {C}} = {\ frac {1} {4 \ pi \ varepsilon _ {0}}}}$ with electrical field constant .${\ displaystyle \ varepsilon _ {0}}$ The ionization energy or binding energy is the sum of the potential energy and kinetic energy of the electron . As always, in stable orbit: is the ionization magnitude always equal to the kinetic energy, or half the potential energy: . This results in the ionization energy for hydrogen in the lowest energy level, also called Rydberg energy : ${\ displaystyle B}$ ${\ displaystyle V}$ ${\ displaystyle T}$ ${\ displaystyle B = V + T}$ ${\ displaystyle 2T = -V}$ ${\ displaystyle B = T + V = -T = V / 2}$ ${\ displaystyle R_ {y} = {\ frac {e ^ {2} k_ {C}} {2a_ {0}}} = {\ frac {v_ {0} ^ {2} m_ {e}} {2} }}$ With

• Drilling radius ${\ displaystyle a_ {0} = {\ tfrac {\ hbar ^ {2}} {e ^ {2} m_ {e} k_ {C}}} = {\ tfrac {\ hbar} {\ alpha m_ {e} c}}}$ • Electron mass ${\ displaystyle m_ {e}}$ • Orbital velocity in the first orbital ${\ displaystyle v_ {0} = \ alpha c}$ • Fine structure constant ${\ displaystyle \ alpha}$ • Speed ​​of Light ${\ displaystyle c}$ • Reduced Planck's quantum of action ${\ displaystyle \ textstyle \ hbar = {\ frac {h} {2 \ pi}}}$ In higher excited orbits, the ionization energy decreases and increases with a higher number of protons in the nucleus, as can be seen from the binding force . In general, according to Bohr's atomic model , the binding energy for a single electron is: ${\ displaystyle F}$ ${\ displaystyle B = {\ frac {e ^ {2} k_ {C} Z} {2r_ {n}}} = {\ frac {v_ {0} ^ {2} m_ {e} Z} {2n ^ { 2}}} = {\ frac {v_ {n} ^ {2} m_ {e} Z} {2}} = {\ frac {Z ^ {2} R_ {y}} {n ^ {2}}} }$ With

• Principal quantum number ${\ displaystyle n}$ • Orbit radius ${\ displaystyle r_ {n} = n ^ {2} a_ {0} / Z}$ • Track speed ${\ displaystyle v_ {n} = v_ {0} / n}$ The first ionization energy increases sharply within a period , even if the increase is discontinuous from left to right. The reason for the increase is the increasing atomic number and the resulting stronger attraction of the electrons by the nucleus. Although the number of electrons in the shell increases to the same extent from left to right within the period, the additional electron is always built into the same shell, the outer shell. The electrons already present there cannot shield the respective incoming electron as strongly from the nuclear charge because they have the same nuclear distance as the newly added electron. The increase in the nuclear charge cannot be compensated for by the increase in the charge of the electron shell, so that the ionization energy increases. The unsteady character of the increase is particularly evident in the transition from nitrogen to oxygen . Here the ionization energy even decreases from left to right. The reasons for such discontinuities can be interpreted with the atomic orbital model . With its half-occupied p-shell, nitrogen has a low-energy, stable electron configuration. A particularly large amount of energy is therefore required to remove an electron. Overall, the ionization energies of the alkali metals represent the minimum and the ionization energies of the noble gases each represent the maximum of the period. These extremes become smaller within a group from top to bottom, since the electron to be removed is located on a new shell according to the shell model of the atom , thus its distance from the core increases and less energy has to be expended to release it from the attraction of the core. Accordingly, the first ionization energy decreases in the transition from one period to the next, e.g. B. from neon to sodium, abruptly. ${\ displaystyle Z}$ ${\ displaystyle r}$ 