FACTOID # 8: Bookworms: Vermont has the highest number of high school teachers per capita and third highest number of librarians per capita.

 Home Encyclopedia Statistics States A-Z Flags Maps FAQ About

 WHAT'S NEW

SEARCH ALL

Search encyclopedia, statistics and forums:

(* = Graphable)

Encyclopedia > Ionization potential

The ionization potential, ionization energy or EI of an atom or molecule is the energy required to remove one mole of electrons from one mole of isolated gaseous atoms or ions. 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 bounded; the greater the ionization energy, the more difficult it is to remove an electron. The ionization potential is an indicator of the reactivity of an element. Elements with low ionization energy tend to be reducing agents and to form salts. For other uses, see Atom (disambiguation). ... 3D (left and center) and 2D (right) representations of the terpenoid molecule atisane. ... Properties The electron (also called negatron, commonly represented as e&#8722;) is a subatomic particle. ... Physical chemistry is the application of physics to macroscopic, microscopic, atomic, subatomic, and particulate phenomena in chemical systems[1]within the field of chemistry traditionally using the principles, practices and concepts of thermodynamics, quantum chemistry, statistical mechanics and kinetics. ... For other uses, see Salt (disambiguation). ...

## Contents

Main article: Ionization energies of the elements

Generally speaking, atomic ionization energies decrease down a group (a.k.a column) of the periodic table, and increase left-to-right across a period. Ionization energy exhibits a strong negative correlation with atomic radius. Successive ionization energies of any given element increase markedly. Particularly dramatic increases occur after any given block of atomic orbitals is exhausted, except when progressing to the next s orbital. This is because, after all the electrons are removed from an orbital, the next ionization energy 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. These tables list the ionization energy in kJ/mol necessary to remove an electron from a neutral atom (first energy), respectively from a singly, doubly, etc. ... For a diagram of the periodic table, see standard periodic table below. ... Atomic radius: Ionic radius Covalent radius Metallic radius van der Waals radius edit Atomic radius, and more generally the size of an atom, is not a precisely defined physical quantity, nor is it constant in all circumstances. ... In chemistry, an atomic orbital is the region in which an electron may be found around a single atom. ... Electron atomic and molecular orbitals In atomic physics and quantum chemistry, the electron configuration is the arrangement of electrons in an atom, molecule, or other physical structure (eg, a crystal). ...

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

Successive ionization energies in kJ/mol (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

In order to determine how many electrons are in the outermost shell of an element, one can use the ionization energy. If, for example, it required 1,500 kJ/mol to remove one electron and required 6,000 kJ/mol to remove another electron 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 octet, it looks to lose one electron. Thus, the first electron is easy to remove and consequently the ionization energy is low. Notice, however, that once the stable octet 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. The joule (IPA: or ) (symbol: J) is the SI unit of energy. ... The mole (symbol: mol) is the SI base unit that measures an amount of substance. ... The electronvolt (symbol eV) is a unit of energy. ... For sodium in the diet, see Edible salt. ... General Name, symbol, number magnesium, Mg, 12 Chemical series alkaline earth metals Group, period, block 2, 3, s Appearance silvery white solid at room temp Standard atomic weight 24. ... General Name, symbol, number aluminium, Al, 13 Chemical series poor metals Group, period, block 13, 3, p Appearance silvery Standard atomic weight 26. ... General Name, Symbol, Number silicon, Si, 14 Chemical series metalloids Group, Period, Block 14, 3, p Appearance as coarse powder, dark grey with bluish tinge Standard atomic weight 28. ... General Name, Symbol, Number phosphorus, P, 15 Chemical series nonmetals Group, Period, Block 15, 3, p Appearance waxy white/ red/ black/ colorless Standard atomic weight 30. ... General Name, Symbol, Number sulfur, S, 16 Chemical series nonmetals Group, Period, Block 16, 3, p Appearance lemon yellow Standard atomic weight 32. ... General Name, symbol, number chlorine, Cl, 17 Chemical series halogens Group, period, block 17, 3, p Appearance yellowish green Standard atomic weight 35. ... General Name, Symbol, Number argon, Ar, 18 Chemical series noble gases Group, Period, Block 18, 3, p Appearance colorless Standard atomic weight 39. ... This article does not cite any references or sources. ...

## Electrostatic explanation

Atomic ionization energy can be predicted by an analysis using electrostatic potential and the Bohr model of the atom, as follows. Electric potential is the potential energy per unit charge associated with a static (time-invariant) electric field, also called the electrostatic potential, typically measured in volts. ... The Bohr model of the hydrogen atom, where negatively charged electrons confined to atomic shells encircle a small positively charged atomic nucleus, and that an electron jump between orbits must be accompanied by an emitted or absorbed amount of electromagnetic energy hÎ½. The orbits that the electrons travel in are...

$V = frac{1}{4piepsilon_0} frac{ne}{a} ,!$

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:

$E = eV = frac{1}{4piepsilon_0} frac{ne^2}{a} ,!$

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. The periodic table of the chemical elements A chemical element, or element, is a type of atom that is defined 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:

$L = |mathbf r times mathbf p| = rmv = nhbar$

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. 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 sophisticated 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. 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. These are related by Pauli's exclusion principle to the antisymmetrized products of the atomic or molecular orbitals. This linear combination is called a configuration interaction expansion of the electronic wavefunction. Fig. ... This article discusses the concept of a wavefunction as it relates to quantum mechanics. ... In quantum mechanics, a Slater determinant (introduced by the American physicist John C. Slater[1]) is an expression describing the wavefunction of a many-fermion system which, by construction, satisfies the Pauli principle by being antisymmetric under an exchange of any pair of fermions. ... The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925. ... In chemistry, an atomic orbital is the region in which an electron may be found around a single atom. ... In quantum chemistry, molecular orbitals are the statistical states electrons can have within molecules. ... Configuration interaction (CI) is a post Hartree-Fock linear variational method for solving the nonrelativistic SchrÃ¶dinger equation within the Born-Oppenheimer approximation for a quantum chemical multi-electron system. ...

In general, calculating the nth ionization energy requires subtracting the energy of a Zn + 1 electron system from the energy of a Zn electron system. Calculating these energies is not simple, but is 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. Computational chemistry is a branch of chemistry that uses the results of theoretical chemistry incorporated into efficient computer programs to calculate the structures and properties of molecules and solids, applying these programs to complement the information obtained by actual chemical experiments, predict hitherto unobserved chemical phenomena, and solve related problems. ... 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 of the highest occupied molecular orbital (the HOMO), and the electron affinity is the negative of the energy...

Share your thoughts, questions and commentary here