IONIZATION ENERGY and WORK FUNCTION (revised)
Material
revised and improved by Lipsa Dorelia
Background and actual interpretation
The energy required to remove one electron from an
isolated, gas-phase atom, when this atom is not hooked up to others like in a
solid or a liquid, is called ionization energy (IE).
M(g) ---->
M+(g) + e-
Generally speaking, ionization
energies decrease down a group of the periodic
table, and increase left-to-right across a period. Ionization energy
exhibits a strong negative correlation with atomic radius.
There is a dependence of ionization energy from nuclear charge, number of
energy levels, and shielding.
As the nuclear charge increases, the attraction
between the nucleus and the electrons increases and it requires more energy to
remove the outermost electron and that means there is higher ionization energy.
Along periodic table it can be observed an increase of ionization energy with
increasing nuclear charge.
In the same column of periodic table, the effect of
increased nuclear charge is balanced by the effect of increased shielding, and
the number of energy levels becomes the predominant factor. With more energy
levels, the outermost electrons (the valence electrons) are further from the
nucleus and are not so strongly attracted to the nucleus. Thus the ionization
energy of the elements decreases as you go down the periodic table because it
is easier to remove the electrons.
Ionization energies differ significantly, depending
on the shell from which the electron is taken. For instance, it takes less
energy to remove a p electron than an s electron, even less
energy to extract a d electron, and the least energy to extract an f
electron. It is considered that s electrons are held closer to the nucleus,
while f electrons are far from the nucleus and less tightly held.
The periodic nature of ionization energy for the
last electron of first 20 elements is presented in fig. 1. With each new period the ionization energy
starts with a low value. Within each period there is an increasing energy value
with some saw teeth. The variation inside a period corresponds to the sublevels
in the energy levels.
Figure 1. Ionization energy
variation
For
H which has only a single electron moving around nucleus there will be a single
value for the ionization potential.
For
other elements, the removal of each subsequent electron requires even more
energy, so a distinct and increasing value of ionization potential is measured
for closer electrons of nucleus; it becomes more difficult to remove additional
electrons because they are closer to the nucleus and thus held more strongly by
net positive charge of nucleus.
More
generally, the nth ionization energy of an atom is the energy
required to strip it of an nth electron after the first n - 1 have already been removed.
In
order to explain the ionization energy, quantum theory does not have a ,,special formula” so, mathematically, the old Bohr
treatment is accepted.
Besides
ionization energy a new physical unit was necessary to be accepted – work
function - based, mainly, on photoelectric experiments. Work function is the
amount of energy needed to remove an electron from a bulk material (solid or
liquid).
In
some scientific texts, the ionization potential and work function of any metal
is considered the same, but their values are different for semiconductors or
insulators. In fact, quantum mechanics define work function as the energy
required to remove an electron from Fermi level to vacuum. The work function is
a characteristic property for any solid face of a substance with a conduction
band (empty or partially filled). For a metal, the Fermi level is inside the
conduction band. For an insulator, the Fermi level lies within the band gap,
indicating an empty conduction band; in this case, the minimum energy to remove
an electron is about the sum of half the band gap, and the work function.
Other texts present an
empirically known correlation between the atomic ionization potential (IP) and
the metal work function (WF)
Experimental facts show that work function depends on
the orientation of the crystal and on crystallization type. For example Ag:4.26,
Ag(110):4.64, Ag(111):4.74.
Why the actual
explanation is erroneous…
In
actual theory of atomic structure, ionization potential plays a secondary
importance. The variation of ionization potential of last outer electron is
used only as support for chemical periodicity. The variation of ionization
potentials of different electrons from the same element or the variation of
ionization potentials of the same inner electron from different elements does
not present any significance in actual quantum mechanic.
In
fact quantum mechanic is able to solve the Schrödinger equation only for hydrogen
or hydrogenous atoms types. Therefore it is an absurd idea, its pretention to
explain the variation of ionization potentials in periodic system. Firstly, in
case of simple hydrogen atom, quantum mechanic must explain why for different
atoms the ionization potential is the same. If electron does not follow a
certain trajectory around nucleus, and its description is like a cloud, the
ionization potential for different atoms must have a statistical distribution.
It is important to emphasize that ionization potential must
play a fundamental role in the atomic structure. This because electrons are
arranged in shells and in every shell again a difference in ionization energy
is observed. In quantum mechanic the difference of ionization energy for the electrons
on the same shell is given by electron spin energy and eventually interaction
between electrons.
In
proposed theory, different values of ionization potential are given due to the
different orbits of electrons movements around nucleus.
In
our calculus a database with ionization potentials found at following address http://spectr-w3.snz.ru was used.
Without
making any supposition about arrangement of electron around nucleus let’s
analyze the ionization potential for isoelectronic
series. By isoelectronic series we mean the same
number of electron but an increasing number of protons respectively neutrons in
nucleus. Due to the limited space for display in tab 1 are presented ionization
potentials for first 15 elements, but the facts presented for these elements
are valid for all elements in periodic system.
Analyzing
the ionization potential of first isoelectronic
series (one electron around nucleus) we observe a quadratic dependency related
to the atomic number Z. The quadratic dependence is easy to be observed for
first isoelectronic series but for other series is
hidden by a constant factor addition in the energy expression. In order to
arrive to a linear dependency we will work with square root of ionization
potential and we will make also some simple mathematical tricks.
We
define relative ionization potential of kth
electron of an element as kth ionization
potential divided by ionization potential of hydrogen electron. For example in
case of hydrogen the relative potential is 1, and for helium we have two
relative ionization potentials; 1,8 for one electron
and 3.99 for the second electron. For other elements the modality of relative
ionization potential calculus are the same. In tab 2, are presented square root
of relative ionization potentials for the first 15 elements.
With
this simple modification, the distribution of square root of relative
ionization potential for first electron (first isoelectronic
series) in different atoms is linearly related to the atomic number Z and this
is observed from tab. 2, even without a graphical representation.
The
variation of square root of relative ionization potentials for first 36 isoelectronic series related to the atomic numbers Z is
presented in fig 1.17 and 1.18; fig. 1.17 is a detailed part of 1.18 and is
presented for a better visualization of ionization potential variations. The
same linear dependence is observed also for higher isoelectronic
series, but a picture with such amount of information doesn’t give any
supplementary information. In pictures the isoelectronic
series are positioned from left to right. For first two isoelectronic
series, two parallel lines with the same slope are obtained when the number
atomic is increased from helium to lead. The second line representing the
energy of second electron in different atoms is a little bit shifted related to
the first isoelectronic series due to a factor which
represent a new appearing interaction. We can observe also a coupling between
energy of first electron and the energy of second electron when we change to
different elements (different atomic numbers); the slope of energy variation
for first two isoelectronic series is constant from
Helium to last element (the checking was made up Z= 90).
As
it is observed the linear dependency is respected for every electron from these
isoelectronic series and also for higher isoelectronic series.
From
the graphical representation of ionization energy we can observe that there is
a coupling of electrons in pairs of minimum 2 electrons with the same slope of
energy variation and for higher Z, a coupling in more pairs of two electrons
having the same slope for energy variation. For example after first pair of
electrons, a number of four pairs (eight electrons orbit) present the same
slope in energy variation. These distributions of ionization potentials
contradict quantum mechanic theory and also wave–corpuscular hypothesis. It is
impossible for an electron having a complicated movement, given as a probability,
to present a linear dependency of ionization potentials.
As
consequences we can suppose, for the moment, that ,,adding”
one or more electrons to a hydrogenoid atom will have
as consequences modification of energy interaction with a simple additional
term; the variation is related to the atomic number.
In the same time for the Moseley low new explanation can be
formulated. The jump of electron from a superior level to another inferior
level, with both energy levels linear dependent on atomic number will produce a
photon with an energy proportional with this difference. In conclusion the ecranation factor due to other electrons from atoms, actual
accepted by quantum mechanic is wrong and the formulation of Moseley low must
be corrected.
Therefore,
the proposed theory, presents a simple and easy to follow variation of
potential ionization in periodic system which suppose a precise trajectory of
electron around nucleus. Quantum theory explanation based on density of
electron probability around nucleus and wave-corpuscle duality are ruled out.
The
linear dependency of relative ionization potential energy is accurate also for
so called d layer and f layer in actual quantum
mechanic. The only difference observed in distribution of relative ionization
potential for different layer is represented by different slope.
A
detailed discussion of these aspects will be made at electron arrangements on multielectron atoms.
Quantum
mechanic collapses completely when, further, the concept of work function is
analyzed.
The
work function value for metals must be equal with ionization energy, because in
this case, based on actual model of metallic bond, electrons are free to move
inside crystal but find a confining potential step U at the boundary of the metal.
In a comparative way, for some
elements, in tab. 1 the values for their first ionization values and work
functions are presented.
Table 1. Work functions and ionization
potential values
|
No. |
Element |
Work function Φ (eV) |
Ionization potential I (eV) |
|
1 |
Silver (Ag) |
4,64 |
7,57 |
|
2 |
Aluminum (Al) |
4,20 |
5,98 |
|
3 |
Gold (Au) |
5,17 |
9,22 |
|
4 |
Boron (B) |
4,45 |
8,298 |
|
5 |
Beryllium (Be) |
4,98 |
9,32 |
|
6 |
Bismuth (Bi) |
4,34 |
7,29 |
|
7 |
Carbon (C) |
5,0 |
11,26 |
|
8 |
Cesium (Ce) |
1,95 |
3,89 |
|
9 |
Iron (Fe) |
4,67 |
7,87 |
|
10 |
Gallium (Ga) |
4,32 |
5,99 |
|
11 |
(Hg) liquid |
4,47 |
10,43 |
|
12 |
Sodium (Na) |
2,36 |
5,13 |
|
13 |
Lithium (Li) |
2,93 |
5,39 |
|
14 |
Potassium |
2,3 |
4,34 |
|
15 |
Selenium (Se) |
5,9 |
9,75 |
|
16 |
Silicon (Si) |
4,85 |
8,15 |
|
17 |
Tin (Sn) |
4,42 |
7,34 |
|
18 |
Germanium (Ge) |
5,0 |
7,89 |
|
19 |
Arsenic (As) |
3,75 |
9,81 |
As is observed, as a general rule,
the ionization energies for all metals are greater then work function. Sodium,
a alkaline metal has a work function of 2,36 eV and a ionization potential value of 5,13 eV and on the other side Aluminium with a ionization potential
of 5,98 eV has a work function of 4,20 eV. For mercury the work function is 4,47
eV and the ionization potential is 10,43 eV. It is very strange how the actual theoreticians didn’t
observe these differences and didn’t make a quantum interpretation of this
difference for metallic structure.
But this is not the nightmare of
quantum mechanics. It is well known that metallic oxides present a lower work
function then metals and even lower then alkaline metals. For example, a
tungsten cathode has a work function equal with 4,54eV and if the tungsten is
covered by thorium oxide the work function is 2,5 eV.
How can explain quantum mechanic
this modification?
There is no explanation and in
fact quantum mechanic predict that tungsten covered by thorium oxide must have
work function greater then pure tungsten. In metal electrons are free to move,
but in metal oxide, according to actual quantum mechanic electrons are part of
ionic or polar covalent bounds and they are not free. Therefore it is not
necessary a deep math treatment to observe the inconsistency of quantum
mechanics.
Further improvements are foreseen
to the present text.