# Ionization energy

In physics and chemistry, ionization energy (American English spelling) or ionisation energy (British English spelling), denoted Ei, is the minimum amount of energy required to remove the most loosely bound electron, the valence electron, of an isolated neutral gaseous atom or molecule. It is quantitatively expressed as

X + energy → X+ + e

where X is any atom or molecule capable of ionization, X+ is that atom or molecule with an electron removed, and e is the removed electron. This is generally an endothermic process. Generally, the closer the outermost electrons are to the nucleus of the atom , the higher the atom's or element's ionization energy.

The sciences of physics and chemistry use different measures of ionization energy. In physics, the unit is the amount of energy required to remove a single electron from a single atom or molecule, expressed as electronvolts. In chemistry, the unit is the amount of energy required for all of the atoms in a mole of substance to lose one electron each: molar ionization energy or enthalpy, expressed as kilojoules per mole (kJ/mol) or kilocalories per mole (kcal/mol).[1]

Comparison of Ei of elements in the periodic table reveals two periodic trends:

1. Ei generally increases as one moves from left to right within a given period (that is, row).
2. Ei generally decreases as one moves from top to bottom in a given group (that is, column).

The latter trend results from the outer electron shell being progressively farther from the nucleus, with the addition of one inner shell per row as one moves down the column.

The nth ionization energy refers to the amount of energy required to remove an electron from the species with a charge of (n-1). For example, the first three ionization energies are defined as follows:

1st ionization energy
X → X+ + e
2nd ionization energy
X+ → X2+ + e
3rd ionization energy
X2+ → X3+ + e

The term ionization potential is an older name for ionization energy,[2] because the oldest method of measuring ionization energy was based on ionizing a sample and accelerating the electron removed using an electrostatic potential. However this term is now considered obsolete.[3] Some factors affecting the ionization energy include:

1. Nuclear charge: the greater the magnitude of nuclear charge the more tightly the electrons are held by the nucleus and hence more will be ionization energy.
2. Number of electron shells: the greater the size of the atom less tightly the electrons are held by the nucleus and ionization energy will be less.
3. Effective nuclear charge (Zeff): the greater the magnitude of electron shielding and penetration the less tightly the electrons are held by the nucleus, the lower the Zeff of the electron, and hence less will be the ionization energy.[4]
4. Type of orbital ionized: the atom having a more stable electronic configuration has less tendency to lose electrons and consequently has high ionization energy.
5. Occupancy of the orbital matters: if the orbital is half or completely filled then it is harder to remove electrons
Periodic trends for ionization energy (Ei) vs. atomic number: note that within each of the seven periods the Ei (colored circles) of an element begins at a minimum for the first column of the periodic table (the alkali metals), and progresses to a maximum for the last column (the noble gases) which are indicated by vertical lines and labelled with a noble gas element symbol, and which also serve as lines dividing the 7 periods. The maximum ionization energy for each row diminishes as one progresses from row 1 to row 7 in a given column, due to the increasing distance of the outer electron shell from the nucleus as inner shells are added.

## Values and trends

Generally, the (n+1)th ionization energy is larger than the nth ionization energy. When the next ionization energy involves removing an electron from the same electron shell, the increase in ionization energy is primarily due to the increased net charge of the ion from which the electron is being removed. Electrons removed from more highly charged ions of a particular element experience greater forces of electrostatic attraction; thus, their removal requires more energy. In addition, when the next ionization energy involves removing an electron from a lower electron shell, the greatly decreased distance between the nucleus and the electron also increases both the electrostatic force and the distance over which that force must be overcome to remove the electron. Both of these factors further increase the ionization energy.

Some values for elements of the third period are given in the following table:

Successive ionization energy values / kJmol−1
(96.485 kJ/mol ≡ 1 eV)
Element First Second Third Fourth Fifth Sixth Seventh
Na 496 4,560
Mg 738 1,450 7,730
Al 577 1,816 2,881 11,600
Si 786 1,577 3,228 4,354 16,100
P 1,060 1,890 2,905 4,950 6,270 21,200
S 999.6 2,260 3,375 4,565 6,950 8,490 27,107
Cl 1,256 2,295 3,850 5,160 6,560 9,360 11,000
Ar 1,520 2,665 3,945 5,770 7,230 8,780 12,000

Large jumps in the successive molar ionization energies occur when passing noble gas configurations. For example, as can be seen in the table above, the first two molar ionization energies of magnesium (stripping the two 3s electrons from a magnesium atom) are much smaller than the third, which requires stripping off a 2p electron from the neon configuration of Mg2+. That electron is much closer to the nucleus than the previous 3s electron.

Ionization energy is also a periodic trend within the periodic table organization. Moving left to right within a period, or upward within a group, the first ionization energy generally increases, with some exceptions such as aluminum and sulfur in the table above. As the nuclear charge of the nucleus increases across the period, the atomic radius decreases and the electron cloud becomes closer towards the nucleus.

## Electrostatic explanation

Atomic ionization energy can be predicted by an analysis using electrostatic potential and the Bohr model of the atom, as follows (note that the derivation uses Gaussian units).

Consider an electron of charge -e and an atomic nucleus with charge +Ze, where Z is the number of protons in the nucleus. According to the Bohr model, if the electron were to approach and bond with the atom, it would come to rest at a certain radius a. The electrostatic potential V at distance a from the ionic nucleus, referenced to a point infinitely far away, is:

${\displaystyle V={\frac {Ze}{a}}\,\!}$

Since the electron is negatively charged, it is drawn inwards by this positive electrostatic potential. The energy required for the electron to "climb out" and leave the atom is:

${\displaystyle E=eV={\frac {Ze^{2}}{a}}\,\!}$

This analysis is incomplete, as it leaves the distance a as an unknown variable. It can be made more rigorous by assigning to each electron of every chemical element a characteristic distance, chosen so that this relation agrees with experimental data.

It is possible to expand this model considerably by taking a semi-classical approach, in which momentum is quantized. This approach works very well for the hydrogen atom, which only has one electron. The magnitude of the angular momentum for a circular orbit is:

${\displaystyle L=|{\boldsymbol {r}}\times {\boldsymbol {p}}|=rmv=n\hbar }$

The total energy of the atom is the sum of the kinetic and potential energies, that is:

${\displaystyle E=T+U={\frac {p^{2}}{2m_{\rm {e}}}}-{\frac {Ze^{2}}{r}}={\frac {m_{\rm {e}}v^{2}}{2}}-{\frac {Ze^{2}}{r}}}$

Velocity can be eliminated from the kinetic energy term by setting the Coulomb attraction equal to the centripetal force, giving:

${\displaystyle T={\frac {Ze^{2}}{2r}}}$

Solving the angular momentum for v and substituting this into the expression for kinetic energy, we have:

${\displaystyle {\frac {n^{2}\hbar ^{2}}{rm_{\rm {e}}}}=Ze^{2}}$

This establishes the dependence of the radius on n. That is:

${\displaystyle r(n)={\frac {n^{2}\hbar ^{2}}{Zm_{\rm {e}}e^{2}}}}$

Now the energy can be found in terms of Z, e, and r. Using the new value for the kinetic energy in the total energy equation above, it is found that:

${\displaystyle E=-{\frac {Ze^{2}}{2r}}}$

At its smallest value, n is equal to 1 and r is the Bohr radius a0 which equals ${\displaystyle {\frac {\hbar ^{2}}{me^{2}}}}$. Now, the equation for the energy can be established in terms of the Bohr radius. Doing so gives the result:

${\displaystyle E=-{\frac {1}{n^{2}}}{\frac {Z^{2}e^{2}}{2a_{0}}}=-{\frac {Z^{2}13.6eV}{n^{2}}}}$

## Quantum-mechanical explanation

According to the more complete theory of quantum mechanics, the location of an electron is best described as a probability distribution within an electron cloud, i.e. atomic orbital. The energy can be calculated by integrating over this cloud. The cloud's underlying mathematical representation is the wavefunction which is built from Slater determinants consisting of molecular spin orbitals. These are related by Pauli's exclusion principle to the antisymmetrized products of the atomic or molecular orbitals.

In general, calculating the nth ionization energy requires calculating the energies of ${\displaystyle Z-n+1}$ and ${\displaystyle Z-n}$ electron systems. Calculating these energies exactly is not possible except for the simplest systems (i.e. hydrogen), primarily because of difficulties in integrating the electron correlation terms. Therefore, approximation methods are routinely employed, with different methods varying in complexity (computational time) and in accuracy compared to empirical data. This has become a well-studied problem and is routinely done in computational chemistry. At the lowest level of approximation, the ionization energy is provided by Koopmans' theorem.

## Vertical and adiabatic ionization energy in molecules

Figure 1. Franck–Condon principle energy diagram. For ionization of a diatomic molecule the only nuclear coordinate is the bond length. The lower curve is the potential energy curve of the neutral molecule, and the upper curve is for the positive ion with a longer bond length. The blue arrow is vertical ionization, here from the ground state of the molecule to the v=2 level of the ion.

Ionization of molecules often leads to changes in molecular geometry, and two types of (first) ionization energy are defined – adiabatic and vertical.[5]

The adiabatic ionization energy of a molecule is the minimum amount of energy required to remove an electron from a neutral molecule, i.e. the difference between the energy of the vibrational ground state of the neutral species (v" = 0 level) and that of the positive ion (v' = 0). The specific equilibrium geometry of each species does not affect this value.

### Vertical ionization energy

Due to the possible changes in molecular geometry that may result from ionization, additional transitions may exist between the vibrational ground state of the neutral species and vibrational excited states of the positive ion. In other words, ionization is accompanied by vibrational excitation. The intensity of such transitions are explained by the Franck–Condon principle, which predicts that the most probable and intense transition corresponds to the vibrational excited state of the positive ion that has the same geometry as the neutral molecule. This transition is referred to as the "vertical" ionization energy since it is represented by a completely vertical line on a potential energy diagram (see Figure).

For a diatomic molecule, the geometry is defined by the length of a single bond. The removal of an electron from a bonding molecular orbital weakens the bond and increases the bond length. In Figure 1, the lower potential energy curve is for the neutral molecule and the upper surface is for the positive ion. Both curves plot the potential energy as a function of bond length. The horizontal lines correspond to vibrational levels with their associated vibrational wave functions. Since the ion has a weaker bond, it will have a longer bond length. This effect is represented by shifting the minimum of the potential energy curve to the right of the neutral species. The adiabatic ionization is the diagonal transition to the vibrational ground state of the ion. Vertical ionization involves vibrational excitation of the ionic state and therefore requires greater energy.

In many circumstances, the adiabatic ionization energy is often a more interesting physical quantity since it describes the difference in energy between the two potential energy surfaces. However, due to experimental limitations, the adiabatic ionization energy is often difficult to determine, whereas the vertical detachment energy is easily identifiable and measurable.

## Analogs of ionization energy to other systems

While the term ionization energy is largely used only for gas-phase atomic or molecular species, there are a number of analogous quantities that consider the amount of energy required to remove an electron from other physical systems.

### Electron binding energy

Electron binding energy is a generic term for the ionization energy that can be used for species with any charge state. For example, the electron binding energy for the chloride ion is the minimum amount of energy required to remove an electron from the chlorine atom when it has a charge of -1. In this particular example, the electron binding energy has the same magnitude as the electron affinity for the neutral chlorine atom. In another example, the electron binding energy refers the minimum amount of energy required to remove an electron from the dicarboxylate dianion O2C(CH2)8CO
2
.

### Work function

Work function is the minimum amount of energy required to remove an electron from a solid surface.

## References

1. ^ "Ionization Energy". ChemWiki. University of California, Davis. 2013-10-02.
2. ^ Cotton, F. Albert; Wilkinson, Geoffrey (1988). Advanced Inorganic Chemistry (5th ed.). John Wiley. p. 1381. ISBN 0-471-84997-9.
3. ^
4. ^ Lang, Peter F.; Smith, Barry C. (2003). "Ionization Energies of Atoms and Atomic Ions". Journal of Chemical Education. 80 (8): 938. Bibcode:2003JChEd..80..938L. doi:10.1021/ed080p938.
5. ^ "The difference between a vertical ionization energy and adiabatic ionization energy". Computational Chemistry Comparison and Benchmark Database. National Institute of Standards and Technology.
Born–Haber cycle

The Born–Haber cycle is an approach to analyze reaction energies. It was named after the two German scientists Max Born and Fritz Haber, who developed it in 1919. It was also independently formulated by Kasimir Fajans. The cycle is concerned with the formation of an ionic compound from the reaction of a metal (often a Group I or Group II element) with a halogen or other non-metallic element such as oxygen.

Born–Haber cycles are used primarily as a means of calculating lattice energy (or more precisely enthalpy), which cannot otherwise be measured directly. The lattice enthalpy is the enthalpy change involved in the formation of an ionic compound from gaseous ions (an exothermic process), or sometimes defined as the energy to break the ionic compound into gaseous ions (an endothermic process). A Born–Haber cycle applies Hess's law to calculate the lattice enthalpy by comparing the standard enthalpy change of formation of the ionic compound (from the elements) to the enthalpy required to make gaseous ions from the elements.

This latter calculation is complex. To make gaseous ions from elements it is necessary to atomise the elements (turn each into gaseous atoms) and then to ionise the atoms. If the element is normally a molecule then we first have to consider its bond dissociation enthalpy (see also bond energy). The energy required to remove one or more electrons to make a cation is a sum of successive ionization energies; for example, the energy needed to form Mg2+ is the ionization energy required to remove the first electron from Mg, plus the ionization energy required to remove the second electron from Mg+. Electron affinity is defined as the amount of energy released when an electron is added to a neutral atom or molecule in the gaseous state to form a negative ion.

The Born–Haber cycle applies only to fully ionic solids such as certain alkali halides. Most compounds include covalent and ionic contributions to chemical bonding and to the lattice energy, which is represented by an extended Born-Haber thermodynamic cycle. The extended Born–Haber cycle can be used to estimate the polarity and the atomic charges of polar compounds.

Dioxygenyl

The dioxygenyl ion, O+2, is a rarely-encountered oxycation in which both oxygen atoms have a formal oxidation state of +​1⁄2. It is formally derived from oxygen by the removal of an electron:

O2 → O+2 + e−The energy change for this process is called the ionization energy of the oxygen molecule. Relative to most molecules, this ionization energy is very high at 1175 kJ/mol. As a result, the scope of the chemistry of O+2 is quite limited, acting mainly as a 1-electron oxidiser.

Ditungsten tetra(hpp)

Tetrakis(hexahydropyrimidinopyrimidine)ditungsten(II), known as ditungsten tetra(hpp), is the name of the coordination compound with the formula W2(hpp)4. This material consists of a pair of tungsten centers linked by the conjugate base of four hexahydropyrimidopyrimidine (hpp) ligands. It adopts a structure sometimes called a Chinese lantern structure or paddlewheel compound, the prototype being copper(II) acetate.

The molecule is of research interest because it has the lowest ionization energy (3.51 eV) of all stable chemical elements or chemical compounds as of the year 2005. This value is even lower than of caesium with 3.89 eV (or 375 kJ/mol) located at the extreme left lower corner of the periodic table (although francium is at a lower position in the periodic table compared to caesium, it has a higher ionization energy and is radioactive) or known metallocene reducing agents such as decamethylcobaltocene with 4.71 eV.

Electron acceptor

An electron acceptor is a chemical entity that accepts electrons transferred to it from another compound. It is an oxidizing agent that, by virtue of its accepting electrons, is itself reduced in the process. Electron acceptors are sometimes mistakenly called electron receptors.

Typical oxidizing agents undergo permanent chemical alteration through covalent or ionic reaction chemistry, resulting in the complete and irreversible transfer of one or more electrons. In many chemical circumstances, however, the transfer of electronic charge from an electron donor may be only fractional, meaning an electron is not completely transferred, but results in an electron resonance between the donor and acceptor. This leads to the formation of charge transfer complexes in which the components largely retain their chemical identities.

The electron accepting power of an acceptor molecule is measured by its electron affinity which is the energy released when filling the lowest unoccupied molecular orbital (LUMO).

The energy required to remove one electron from the electron donor is its ionization energy (I). The energy liberated by attachment of an electron to the electron acceptor is the negative of its electron affinity (A). The overall system energy change (ΔE) for the charge transfer is then ${\displaystyle {\Delta }E=I-A\,}$. For an exothermic reaction, the energy liberated is of interest and is equal to ${\displaystyle -{\Delta }E=A-I\,}$.

In chemistry, a class of electron acceptors that acquire not just one, but a set of two paired electrons that form a covalent bond with an electron donor molecule, is known as a Lewis acid. This phenomenon gives rise to the wide field of Lewis acid-base chemistry. The driving forces for electron donor and acceptor behavior in chemistry is based on the concepts of electropositivity (for donors) and electronegativity (for acceptors) of atomic or molecular entities.

Electronegativity

Electronegativity, symbol χ, is a chemical property that describes the tendency of an atom to attract a shared pair of electrons (or electron density) towards itself. An atom's electronegativity is affected by both its atomic number and the distance at which its valence electrons reside from the charged nucleus. The higher the associated electronegativity number, the more an atom or a substituent group attracts electrons towards itself.

On the most basic level, electronegativity is determined by factors like the nuclear charge (the more protons an atom has, the more "pull" it will have on electrons) and the number/location of other electrons present in the atomic shells (the more electrons an atom has, the farther from the nucleus the valence electrons will be, and as a result the less positive charge they will experience—both because of their increased distance from the nucleus, and because the other electrons in the lower energy core orbitals will act to shield the valence electrons from the positively charged nucleus).

The opposite of electronegativity is electropositivity: a measure of an element's ability to donate electrons.

The term "electronegativity" was introduced by Jöns Jacob Berzelius in 1811,

though the concept was known even before that and was studied by many chemists including Avogadro.

In spite of its long history, an accurate scale of electronegativity was not developed until 1932, when Linus Pauling proposed an electronegativity scale, which depends on bond energies, as a development of valence bond theory. It has been shown to correlate with a number of other chemical properties. Electronegativity cannot be directly measured and must be calculated from other atomic or molecular properties. Several methods of calculation have been proposed, and although there may be small differences in the numerical values of the electronegativity, all methods show the same periodic trends between elements.

The most commonly used method of calculation is that originally proposed by Linus Pauling. This gives a dimensionless quantity, commonly referred to as the Pauling scale (χr), on a relative scale running from around 0.7 to 3.98 (hydrogen = 2.20). When other methods of calculation are used, it is conventional (although not obligatory) to quote the results on a scale that covers the same range of numerical values: this is known as an electronegativity in Pauling units.

As it is usually calculated, electronegativity is not a property of an atom alone, but rather a property of an atom in a molecule. Properties of a free atom include ionization energy and electron affinity. It is to be expected that the electronegativity of an element will vary with its chemical environment, but it is usually considered to be a transferable property, that is to say that similar values will be valid in a variety of situations.

Caesium is the least electronegative element in the periodic table (=0.79), while fluorine is most electronegative (=3.98). Francium and caesium were originally both assigned 0.7; caesium's value was later refined to 0.79, but no experimental data allows a similar refinement for francium. However, francium's ionization energy is known to be slightly higher than caesium's, in accordance with the relativistic stabilization of the 7s orbital, and this in turn implies that francium is in fact more electronegative than caesium.

Hartree

The hartree (symbol: Eh or Ha), also known as the Hartree energy, is the atomic unit of energy, named after the British physicist Douglas Hartree. It is defined as

2R∞hc, where R∞ is the Rydberg constant, h is the Planck constant and c is the speed of light.

The 2014 CODATA recommended value is Eh = 4.359 744 650(54)×10−18 J = 27.211 386 02(17) eV.The hartree energy is approximately the electric potential energy of the hydrogen atom in its ground state and, by the virial theorem, approximately twice its ionization energy; the relationships are not exact because of the finite mass of the nucleus of the hydrogen atom and relativistic corrections.

The hartree is usually used as a unit of energy in atomic physics and computational chemistry: for experimental measurements at the atomic scale, the electronvolt (eV) or the reciprocal centimetre (cm−1) are much more widely used.

Ion

An ion () is an atom or molecule that has a non-zero net electrical charge. Since the charge of the electron (considered "negative" by convention) is equal and opposite to that of the proton (considered "positive" by convention), the net charge of an ion is non-zero due to its total number of electrons being unequal to its total number of protons. A cation is a positively charged ion, with fewer electrons than protons, while an anion is negatively charged, with more electrons than protons. Because of their opposite electric currents, cations and anions attract each other and readily form ionic compounds.

Ions consisting of only a single atom are termed atomic or monatomic ions, while two or more atoms form molecular ions or polyatomic ions. In the case of physical ionization in a medium, such as a gas, "ion pairs" are created by ion collisions, where each generated pair consists of a free electron and a positive ion. Ions are also created by chemical interactions, such as the dissolution of a salt in liquids, or by other means, such as passing a direct current through a conducting solution, dissolving an anode via ionization.

Ionization

Ionization or ionisation, is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule is called an ion. Ionization can result from the loss of an electron after collisions with subatomic particles, collisions with other atoms, molecules and ions, or through the interaction with electromagnetic radiation. Heterolytic bond cleavage and heterolytic substitution reactions can result in the formation of ion pairs. Ionization can occur through radioactive decay by the internal conversion process, in which an excited nucleus transfers its energy to one of the inner-shell electrons causing it to be ejected.

Kilocalorie per mole

The kilocalorie per mole is a unit to measure an amount of energy per number of molecules, atoms, or other similar particles. It is defined as one kilocalorie of energy (1000 thermochemical gram calories) per one mole of substance, that is, per Avogadro’s number of particles. It is abbreviated "kcal/mol" or "kcal mol−1". As typically measured, one kcal/mol represents a temperature increase of one degree Celsius in one liter of water (with a mass of 1kg) resulting from the reaction of one mole of reagents.

In SI units, one kilocalorie per mole is equal to 4.184 kilojoules per mole, or 6.9477×10−21 joules per molecule, or 0.043 eV per molecule. At room temperature (25 °C, 77 °F, or 298.15 K) it is equal to 1.688 units in the kT term of Boltzmann's equation.

Even though it is not an SI unit, the kilocalorie per mole is still widely used in chemistry for thermodynamical quantities such as thermodynamic free energy, heat of vaporization, heat of fusion and ionization energy, due to the ease with which it can be calculated based on the units of measure typically employed in quantifying a chemical reaction, especially in aqueous solution. Typically but not exclusively, kcal/mol are used in the United States, whereas kJ/mol are preferred elsewhere.

Koopmans' theorem

Koopmans' theorem states that in closed-shell Hartree–Fock theory (HF), the first ionization energy of a molecular system is equal to the negative of the orbital energy of the highest occupied molecular orbital (HOMO). This theorem is named after Tjalling Koopmans, who published this result in 1934.Koopmans' theorem is exact in the context of restricted Hartree–Fock theory if it is assumed that the orbitals of the ion are identical to those of the neutral molecule (the frozen orbital approximation). Ionization energies calculated this way are in qualitative agreement with experiment – the first ionization energy of small molecules is often calculated with an error of less than two electron volts. Therefore, the validity of Koopmans' theorem is intimately tied to the accuracy of the underlying Hartree–Fock wavefunction. The two main sources of error are orbital relaxation, which refers to the changes in the Fock operator and Hartree–Fock orbitals when changing the number of electrons in the system, and electron correlation, referring to the validity of representing the entire many-body wavefunction using the Hartree–Fock wavefunction, i.e. a single Slater determinant composed of orbitals that are the eigenfunctions of the corresponding self-consistent Fock operator.

Empirical comparisons with experimental values and higher-quality ab initio calculations suggest that in many cases, but not all, the energetic corrections due to relaxation effects nearly cancel the corrections due to electron correlation.A similar theorem exists in density functional theory (DFT) for relating the exact first vertical ionization energy and electron affinity to the HOMO and LUMO energies, although both the derivation and the precise statement differ from that of Koopmans' theorem. Ionization energies calculated from DFT orbital energies are usually poorer than those of Koopmans' theorem, with errors much larger than two electron volts possible depending on the exchange-correlation approximation employed. The LUMO energy shows little correlation with the electron affinity with typical approximations. The error in the DFT counterpart of Koopmans' theorem is a result of the approximation employed for the exchange correlation energy functional so that, unlike in HF theory, there is the possibility of improved results with the development of better approximations.

Lyman continuum photons

Lyman continuum photons (abbrev. LyC), shortened to Ly continuum photons or Lyc photon, are the photons emitted from stars at photon energies above the Lyman limit. Hydrogen is ionized by absorbing LyC. Working off of Victor Schumann's discovery of ultraviolet light, from 1906 to 1914, Theodore Lyman observed that atomic hydrogen absorbs light only at specific frequencies (or wavelengths) and the Lyman series is thus named after him. All the wavelengths in the Lyman series are in the ultraviolet band. This quantized absorption behavior occurs only up to an energy limit, known as the ionization energy. In the case of neutral atomic hydrogen, the minimum ionization energy is equal to the Lyman limit, where the photon has enough energy to completely ionize the atom, resulting in a free proton and a free electron. Above this energy (below this wavelength), all wavelengths of light may be absorbed. This forms a continuum in the energy spectrum; the spectrum is continuous rather than composed of many discrete lines, which are seen at lower energies.

The Lyman limit is at the wavelength of 91.2 nm (912 Å), corresponding to a frequency of 3.29 million GHz and a photon energy of 13.6 eV. LyC energies are mostly in the ultraviolet C portion of the electromagnetic spectrum (see Lyman series). Although X-rays and gamma-rays will also ionize a hydrogen atom, there are far fewer of them emitted from a star's photosphere—LyC are predominantly UV-C. The photon absorption process leading to the ionization of atomic hydrogen can occur in reverse: an electron and a proton can collide and form atomic hydrogen. If the two particles were traveling slowly (so that kinetic energy can be ignored), then the photon the atom emits upon its creation will theoretically be 13.6 eV (in reality, the energy will be less if the atom is formed in an excited state). At faster speeds, the excess (kinetic) energy is radiated (but momentum must be conserved) as photons of lower wavelength (higher energy). Therefore, photons with energies above 13.6 eV are emitted by the combination of energetic protons and electrons forming atomic hydrogen, and emission from photoionized hydrogen.

Molar ionization energies of the elements

These tables list values of molar ionization energies, measured in kJ mol−1. This is the energy per mole necessary to remove electrons from gaseous atoms or atomic ions. The first molar ionization energy applies to the neutral atoms. The second, third, etc., molar ionization energy applies to the further removal of an electron from a singly, doubly, etc., charged ion. For ionization energies measured in the unit eV, see Ionization energies of the elements (data page). All data from rutherfordium onwards is predicted.

Muonium

Muonium is an exotic atom made up of an antimuon and an electron, which was discovered in 1960 by Vernon W. Hughes

and is given the chemical symbol Mu. During the muon's 2.2 µs lifetime, muonium can enter into compounds such as muonium chloride (MuCl) or sodium muonide (NaMu). Due to the mass difference between the antimuon and the electron, muonium (μ+e−) is more similar to atomic hydrogen (p+e−) than positronium (e+e−). Its Bohr radius and ionization energy are within 0.5% of hydrogen, deuterium, and tritium, and thus it can usefully be considered as an exotic light isotope of hydrogen.Although muonium is short-lived, physical chemists study it using muon spin spectroscopy (μSR), a magnetic resonance technique analogous to nuclear magnetic resonance (NMR) or electron spin resonance (ESR) spectroscopy. Like ESR, μSR is useful for the analysis of chemical transformations and the structure of compounds with novel or potentially valuable electronic properties. Muonium is usually studied by muon spin rotation, in which the Mu atom's spin precesses in a magnetic field applied transverse to the muon spin direction (since muons are typically produced in a spin-polarized state from the decay of pions), and by avoided level crossing (ALC), which is also called level crossing resonance (LCR). The latter employs a magnetic field applied longitudinally to the polarization direction, and monitors the relaxation of muon spins caused by "flip/flop" transitions with other magnetic nuclei.

Because the muon is a lepton, the atomic energy levels of muonium can be calculated with great precision from quantum electrodynamics (QED), unlike in the case of hydrogen, where the precision is limited by uncertainties related to the internal structure of the proton. For this reason, muonium is an ideal system for studying bound-state QED and also for searching for physics beyond the standard model.

Periodic table

The periodic table, also known as the periodic table of elements, is a tabular display of the chemical elements, which are arranged by atomic number, electron configuration, and recurring chemical properties. The structure of the table shows periodic trends. The seven rows of the table, called periods, generally have metals on the left and non-metals on the right. The columns, called groups, contain elements with similar chemical behaviours. Six groups have accepted names as well as assigned numbers: for example, group 17 elements are the halogens; and group 18 are the noble gases. Also displayed are four simple rectangular areas or blocks associated with the filling of different atomic orbitals.

The organization of the periodic table can be used to derive relationships between the various element properties, and also to predict chemical properties and behaviours of undiscovered or newly synthesized elements. Russian chemist Dmitri Mendeleev published the first recognizable periodic table in 1869, developed mainly to illustrate periodic trends of the then-known elements. He also predicted some properties of unidentified elements that were expected to fill gaps within the table. Most of his forecasts proved to be correct. Mendeleev's idea has been slowly expanded and refined with the discovery or synthesis of further new elements and the development of new theoretical models to explain chemical behaviour. The modern periodic table now provides a useful framework for analyzing chemical reactions, and continues to be widely used in chemistry, nuclear physics and other sciences.

The elements from atomic numbers 1 (hydrogen) through 118 (oganesson) have been discovered or synthesized, completing seven full rows of the periodic table. The first 94 elements all occur naturally, though some are found only in trace amounts and a few were discovered in nature only after having first been synthesized. Elements 95 to 118 have only been synthesized in laboratories or nuclear reactors. The synthesis of elements having higher atomic numbers is currently being pursued: these elements would begin an eighth row, and theoretical work has been done to suggest possible candidates for this extension. Numerous synthetic radionuclides of naturally occurring elements have also been produced in laboratories.

Periodic trends

Periodic trends are specific patterns in the properties of chemical elements that are revealed in the periodic table of elements. Major periodic trends include electronegativity, ionization energy, electron affinity, atomic radius, ionic radius, metallic character, and chemical reactivity.

Periodic trends arise from the changes in the atomic structure of the chemical elements within their respective periods (horizontal rows) and groups in the periodic table. These trends enable the chemical elements to be organized in the periodic table based on their atomic structures and properties.

Some exceptions to these trends exist, such as that of ionization energy in Groups 3 and 6.

Photobiology

Photobiology is the scientific study of the interactions of light (technically, non-ionizing radiation) and living organisms. The field includes the study of photophysics, photochemistry, photosynthesis, photomorphogenesis, visual processing, circadian rhythms, photomovement, bioluminescence, and ultraviolet radiation effects.The division between ionizing radiation and non-ionizing radiation is typically considered to be a photon energy greater than 10 eV, which approximately corresponds to both the first ionization energy of oxygen, and the ionization energy of hydrogen at about 14 eV.

Photoemission spectroscopy

Photoemission spectroscopy (PES), also known as photoelectron spectroscopy, refers to energy measurement of electrons emitted from solids, gases or liquids by the photoelectric effect, in order to determine the binding energies of electrons in a substance. The term refers to various techniques, depending on whether the ionization energy is provided by an X-ray photon, an EUV photon, or an ultraviolet photon. Regardless of the incident photon beam, however, all photoelectron spectroscopy revolves around the general theme of surface analysis by measuring the ejected electrons.

Rydberg state

The Rydberg states of an atom or molecule are electronically excited states with energies that follow the Rydberg formula as they converge on an ionic state with an ionization energy. Although the Rydberg formula was developed to describe atomic energy levels, it has been used to describe many other systems that have electronic structure roughly similar to atomic hydrogen. In general, at sufficiently high principal quantum numbers, an excited electron - ionic core system will have the general character of a hydrogenic system and the energy levels will follow the Rydberg formula. Rydberg states have energies converging on the energy of the ion. The ionization energy threshold is the energy required to completely liberate an electron from the ionic core of an atom or molecule. In practice, a Rydberg wave packet is created by a laser pulse on a hydrogenic atom and thus populates a superposition of Rydberg states. Modern investigations using pump-probe experiments show molecular pathways – e.g. dissociation of (NO)2 – via these special states.

Thermal ionization

Thermal ionization, also known as surface ionization or contact ionization, is a physical process whereby the atoms are desorbed from a hot surface, and in the process are spontaneously ionized.

Thermal ionization is used to make simple ion sources, for mass spectrometry and for generating ion beams. Thermal ionization has seen extensive use in determining atomic weights, in addition to being used in many geological/nuclear applications

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