Ionization potential

Ionization energies of neutral elements.

The ionization potential, ionization energy or E_I of an atom or molecule is the energy required to remove one mole of electrons from one mole of isolated gaseous atoms or ions. History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J More generally, the nth ionization energy is the energy required to strip it of an nth mole of electrons after the first $n - 1$ mole of electrons have already been removed. It is considered in physical chemistry as 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. Physical chemistry, is the application of Physics to macroscopic microscopic atomic subatomic and particulate phenomena in chemical systems It is mostly defined as a large The ionization potential is an indicator of the reactivity of an element. Elements with a low ionization energy tend to be reducing agents and to form salts. Salt is a Dietary mineral composed primarily of Sodium chloride that is essential for Animal life but toxic to most land plants

Values and trends

Main article: Ionization energies of the elements

The next ionization energy involves removing an electron from an orbital closer to the nucleus. These tables list the Ionization energy in kJ/mol necessary to remove one mole of Electrons from one mole of neutral gaseous Atoms (first energy respectively 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/mol (96. The joule (written in lower case ˈdʒuːl or /ˈdʒaʊl/ (symbol J) is the SI unit of Energy measuring heat, Electricity The mole (symbol mol) is a unit of Amount of substance: it is an SI base unit, and almost the only unit to be used to measure this 485 kJ/mol = 1 eV)
Element	First	Second	Third	Fourth	Fifth	Sixth	Seventh
Na	496	4,560
Mg	736	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. Sodium (ˈsoʊdiəm is an element which has the symbol Na( Latin natrium, from Arabic natrun) atomic number 11 atomic mass 22 Magnesium (mægˈniːziəm is a Chemical element with the symbol Mg, Atomic number 12 Atomic weight 24 WikipediaNaming Silicon (ˈsɪlɪkən or /ˈsɪlɪkɒn/ silicium is the Chemical element that has the symbol Si and Atomic number 14 Phosphorus, (ˈfɒsfərəs is the Chemical element that has the symbol P and Atomic number 15 Sulfur or sulphur (ˈsʌlfɚ see spelling below) is the Chemical element that has the Atomic number 16 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

In order to determine how many electrons are in the outermost shell of an element, one can use the ionization energy. Chlorine (ˈklɔriːn from the Greek word 'χλωρóς' ( khlôros, meaning 'pale green' is the Chemical element with Atomic number 17 and This article pertains to the chemical element For other uses see Argon (disambiguation. If, for example, it required 1,500 kJ/mol to remove one mole of electrons and required 6,000 kJ/mol to remove another mole of electrons and then 5,000 kJ/mol, etc. this means that the element had one electron in its outermost shell. This means that the element is a metal and in order for this element to achieve a stable complete outer shell, it looks to destroy one electron. The M acro E xpansion T emplate A ttribute L anguage complements TAL, providing macros which allow the reuse of code across Thus, the first electron is easy to remove and consequently the ionization energy is low. Notice, however, that once the stable complete outer shell has been formed, it becomes much more difficult to remove the next electron. If that electron can be removed the consequent one can be removed a bit more easily.

Electrostatic explanation

Atomic ionization energy can be predicted by an analysis using electrostatic potential and the Bohr model of the atom, as follows. At a point in space the electric potential is the Potential energy per unit of charge that is associated with a static (time-invariant Electric field In Atomic physics, the Bohr model created by Niels Bohr depicts the Atom as a small positively charged nucleus surrounded by Electrons

Consider an electron of charge -e, and an ion with charge +ne, where n is the number of electrons missing from the ion. The elementary charge, usually denoted e, is the Electric charge carried by a single Proton, or equivalently the negative of the electric charge carried An ion is an Atom or Molecule which has lost or gained one or more Valence electrons giving it a positive or negative electrical charge An ion is an Atom or Molecule which has lost or gained one or more Valence electrons giving it a positive or negative electrical charge According to the Bohr model, if the electron were to approach and bind with the atom, it would come to rest at a certain radius a. In Atomic physics, the Bohr model created by Niels Bohr depicts the Atom as a small positively charged nucleus surrounded by Electrons The electrostatic potential V at distance a from the ionic nucleus, referenced to a point infinitely far away, is:

$V = \frac{1}{4\pi\epsilon_0} \frac{ne}{a} \,\!$

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

$E = eV = \frac{1}{4\pi\epsilon_0} \frac{ne^2}{a} \,\!$

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. A chemical element is a type of Atom that is distinguished by its Atomic number; that is by the number of Protons in its nucleus.

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:

$L = |\mathbf r \times \mathbf p| = rmv = n\hbar$

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

$E = T + U = \frac{p^2}{2m_e} - \frac{ke^2}{r} = \frac{m_e v^2}{2} - \frac{ke^2}{r}$

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

$T = \frac{ke^2}{2r}$

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:

$E = - \frac{ke^2}{2r}$

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

$\frac{n^2 \hbar^2}{rm_e} = ke^2$

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

$r(n) = \frac{n^2 \hbar^2}{km_e e^2}$

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. In the Bohr model of the structure of an Atom, put forward by Niels Bohr in 1913 Electrons orbit a central nucleus. Doing so gives the result:

$E = - \frac{1}{n^2} \frac{ke^2}{2a_0} = - \frac{13.6eV}{n^2}$

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

$E = - \frac{Z^2}{n^2} \frac{ke^2}{2a_0} = - \frac{13.6 Z^2}{n^2}eV$

Quantum-mechanical explanation

According to the more elegant theory of quantum mechanics, 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. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons The energy can be calculated by integrating over this cloud. The cloud's underlying mathematical representation is the wavefunction which is built from a Slater determinant consisting of molecular spin orbitals. A wave function or wavefunction is a mathematical tool used in Quantum mechanics to describe any physical system In Quantum mechanics, a Slater determinant is an expression which describes the Wavefunction of a multi- Fermionic system that satisfies anti-symmetry These are related by Pauli's exclusion principle to the antisymmetrized products of the atomic or molecular orbitals. The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925 An atomic orbital is a Mathematical function that describes the wave-like behavior of an electron in an atom In Chemistry, a molecular orbital (or MO) is a region in which an Electron may be found in a Molecule. This linear combination is called a configuration interaction expansion of the electronic wavefunction. Configuration interaction ( CI) is a Post Hartree-Fock linear variational method for solving the nonrelativistic Schrödinger equation within the

In general, calculating the nth ionization energy requires subtracting the energy of a $Z - n + 1$ electron system from the energy of a $Z - n$ electron system. Calculating these energies is not simple, but is a well-studied problem and is routinely done in computational chemistry. Computational chemistry is a branch of Chemistry that uses computers to assist in solving chemical problems At the lowest level of approximation, the ionization energy is provided by 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