Ionization potential

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Ionization potential

The ionization potential, ionization energy or E_I of an atom

Atom

|-! bgcolor=gray | Properties|-||}The atom is a basic unit of matter consisting of a dense, central atomic nucleus surrounded by a electron cloud of electric charge electrons....
or molecule

Molecule

In chemistry, a molecule is defined as a sufficiently stable, electric charge neutral group of at least two atoms in a definite arrangement held together by very strong chemical bonds....
is the energy

Energy

In physics, energy is a scalar physical quantity that describes the amount of Work_ that can be performed by a force. Energy is an attribute of objects and systems that is subject to a conservation law....
required to remove one mole of electrons from one mole of gaseous atoms or ions. More generally, the nth ionization energy is the energy required to strip it of the nth electron after the first electrons have been removed. It is considered a measure of the "reluctance" of an atom or ion to surrender an electron, or the "strength" by which the electron is bound; the greater the ionization energy, the more difficult it is to remove an electron.

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Values and trends

Main article: Ionization energies of the elements

Ionization energies of the elements

These tables list the ionization energy in kilojoule per mole necessary to remove one mole of electrons from one mole of neutral gaseous atoms , respectively from a singly, doubly, etc....

Generally the n+1st ionization energy is larger than the nth ionization energy. The next ionization energy (the n+1st) involves removing an electron from an orbital closer to the nucleus. Electrons in the closer orbital experience greater forces of electrostatic attraction, and thus, require more energy to be removed.

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

Successive ionization energies in kJ
Joule

The **joule** is the SI derived unit of energy in the International System of Units. It is defined as:One joule is the amount of energy required to perform the following actions:...
/mol
Mole (unit)

The **mole** is a Units of measurement of amount of substance: it is an SI base unit, and one of the few units used to measure this physical quantity....
(96.485 kJ/mol = 1 eV)
Element	First	Second	Third	Fourth	Fifth	Sixth	Seventh
Na Sodium Sodium is an element which has the symbol Na , atomic number 11, atomic mass 23 amu , and a common oxidation number +1. Sodium is a soft, silvery white, highly reactive element and is a member of the alkali metals within "group 1" ....	496	4,560
Mg Magnesium Magnesium is a chemical element with the symbol Mg, atomic number 12, atomic weight 24.3050 and common oxidation number +2.Magnesium, an alkaline earth metal, is the ninth most abundance of the chemical elements in the universe by mass....	738	1,450	7,730
Al Aluminium Aluminium or aluminum is a silvery white and ductile member of the boron group of chemical elements. It has the symbol Al; its atomic number is 13....	577	1,816	2,881	11,600
Si Silicon Silicon is the most common metalloid. It is a chemical element, which has the symbol Si and atomic number 14. The atomic mass is 28.0855....	786	1,577	3,228	4,354	16,100
P Phosphorus Phosphorus is the chemical element that has the symbol P and atomic number 15. The name comes from the and . A Valency nonmetal of the nitrogen group, phosphorus is commonly found in inorganic phosphate minerals....	1,060	1,890	2,905	4,950	6,270	21,200
S Sulfur Sulfur or sulphur is the chemical element that has the atomic number 16. It is denoted with the symbol S. It is an abundant Valence non-metal....	999.6	2,260	3,375	4,565	6,950	8,490	27,107
Cl Chlorine Chlorine...	1,256	2,295	3,850	5,160	6,560	9,360	11,000
Ar Argon Argon is a chemical element designated by the symbol Ar. Argon has atomic number 18 and is the third element in group 18 of the periodic table ....	1,520	2,665	3,945	5,770	7,230	8,780	12,000

Large jumps in the successive ionization energies occur when passing noble gas

Noble gas

|}The noble gases are a group of chemical elements with very similar properties: under standard conditions, they are all odorless, colorless, monatomic gases, with a very low chemical reactivity....
configurations. For example, as can be seen in the table above, the first two 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 very stable neon

Neon

Neon is the chemical element that has the symbol Ne and atomic number 10. Although a very common element in the universe, it is rare on Earth....
configuration of Mg²⁺.

Electrostatic explanation

Atomic ionization energy can be predicted by an analysis using electrostatic potential and the Bohr model

Bohr model

Ion

An ion is an atom or molecule which has lost or gained one or more electrons, giving it a positive or negative electrical charge. According to the Bohr_model this will be from or in the outer shield 'n'....
with charge +ne, where n is the number of electrons missing from the ion

Ion

Bohr model

In atomic physics, the Bohr model created by Niels Bohr depicts the atom as a small, positively charged atomic nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with electrostatic forces providing attraction, rather than gravity....
, if the electron were to approach and bind 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:

Since the electron is negatively charged, it is drawn to this positive potential. (The value of this potential is called the ionisation potential). The energy required for it to "climb out" and leave the atom is:

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

Chemical element

A chemical element is a type of atom that is distinguished by its atomic number; that is, by the number of protons in its atomic nucleus. The term is also used to refer to a pure chemical Chemical substance composed of atoms with the same number of protons....
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:

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

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

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

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

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

At its smallest value, n is equal to 1 and r is the Bohr radius a₀. Now, the equation for the energy can be established in terms of the Bohr radius

Bohr radius

In the Bohr model of the structure of an atom, put forward by Niels Bohr in 1913, electrons orbit a central atomic nucleus. The model says that the electrons orbit only at certain distances from the nucleus, depending on their energy....
. Doing so gives the result:

This can be expanded to larger nuclei by incorporating the atomic number into the equation.

Quantum-mechanical explanation

According to the more complete theory of quantum mechanics

Quantum mechanics

Quantum mechanics is a set of principles underlying the most fundamental known description of all physical systems at the microscopic scale . Notable amongst these principles are both a dual wave-like and particle-like behavior of matter and radiation, and prediction of probabilities in situations where classical physics predicts certaintie...
, the location of an electron is best described as a "cloud" of likely locations that ranges near and far from the nucleus, or in other words a probability distribution. The energy can be calculated by integrating over this cloud. The cloud's underlying mathematical representation is the wavefunction

Wavefunction

A wave function or wavefunction is a mathematical tool used in quantum mechanics to describe any physical system. It is a function from a mathematical space that maps the possible states of the system into the complex numbers....
which is built from Slater determinant

Slater determinant

In quantum mechanics, a Slater determinant is an expression which describes the wavefunction of a multi-fermionic system that satisfies Skew-symmetric matrix requirements and subsequently the Pauli exclusion principle by changing Plus and minus signs upon exchange of fermions....
s consisting of molecular spin orbitals. These are related by Pauli's exclusion principle to the antisymmetrized products of the atomic

Atomic orbital

An atomic orbital is a mathematical function that describes the wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus....
or molecular orbitals. This linear combination is called a configuration interaction

Configuration interaction

Configuration interaction is a post Hartree-Fock linear variational method for solving the nonrelativistic Schr?dinger equation within the Born-Oppenheimer approximation for a Quantum chemistry multi-electron system....
expansion of the electronic wavefunction.

In general, calculating the nth ionisation energy requires calculating the energies of and electron systems. Calculating these energies is not simple, but is a well-studied problem and is routinely done in computational chemistry

Computational chemistry

Computational chemistry is a branch of chemistry that uses computers to assist in solving chemical problems. It uses the results of theoretical chemistry, incorporated into efficient computer programs, to calculate the structures and properties of molecules and solids....
. At the lowest level of approximation, the ionisation energy is provided by Koopmans' theorem

Koopmans' theorem

Koopmans' theorem is an approximation in molecular orbital theory, such as density functional theory, or Hartree-Fock theory, in which the first ionization energy of a molecule is equal to the energy multiplied by -1, of the highest occupied molecular orbital , and the electron affinity is the negative of the energy of the lowest unoccupied,...
.

Ionization potential

Values and trends

Electrostatic explanation

Quantum-mechanical explanation

See also