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ATOMIC THEORY AND QUANTUM MECHANICS
Objectives :
After learning this chapter, you are expected to be able to :
- Explain the atomic theory according to Dalton, Thomson, and Rutherford
- Explain the atomic theory of quantum mechanics
- Explain and determine the quantum numbers
- Describe the atomic orbital shapes
- Explain the atomic shell and subshell and their relations to the quantum numbers
- Use Aufbau principle, Pauli exclusion principle, and Hund’s rule in writing an electron configuration and describing the orbital diagram
- Determine the placement of an element at the periodic table based on its electron configuration
A. Dalton’s Atomic Model
At the beginning of the 19-th century (in 1808), a British chemist and physicist, John Dalton (1766-1844) studied carefully how the different elements, such as hydrogen and oxygen, could combine to make other substances, like water. In his book A New System of Chemical Philosophy, Dalton made two assertions about atoms, those are :
a. Atoms of each element are identical to one another, but different from the atoms of all other elements.
b. Atoms of different elements can combine to form more complex substance.
Dalton’s idea that different elements had different atoms was unlike the Democritus’ s idea about atoms. The properties of Dalton’s atoms determined the chemical and physical properties of a substance. For example, carbon atoms can form both diamonds and graphite atoms because both substances are composed of the same chemical element. Whereas, according to the Democritus’ s idea about atom, diamond atoms would be very different from graphite atoms.
Dalton observed that two elements can combine in more than one way. For example, modern scientist know that carbon monoxide (CO) and carbon dioxide (CO2) are both compounds of carbon and oxygen. According to Dalton’s experiments, the quantities of an element needed to compose the different compounds are always whole-number multiples of one another. For example, oxygen needed to form a liter of CO. Based on the result of his experiment. Dalton concluded that compounds were created when atoms of pure elements joined together to form a unit called molecule in fixed proportions. This Dalton’s conclusion is also called doubled multiple law.
B. Thomson’s Atomic Model
Since the found of electron as the elementary negatively charged particle, so the validity of Dalton’s atomic theory begin to the questionable. In 1899, a British physicist. Sir Joseph Thomson, proposed an atomic model called raisin plum pudding model. Thomson described atom as a positively charged sphere containing several negatively charged particles called electrons. The electrons are scattered in the sphere like raisins in a plum pudding.
Figure 1. Thomson’s atomic model (raisin plum pudding model)
C. Rutherford’s Atomic Model
In 1991, Ernest Rutherford, Geiger and Marsden was doing experiment by shooting the alpha particle (α) on the thin plate of gold to prove Thomson’s atomic theory. From the result of experiment, Rutherford proposed a theory or model of atom as follows.
.a. The atom consist of atomic nuclei which is positively charged. The nucleus contains almost entire mass of the atom and surrounded by electrons which are negatively charged as in solar system model.
b. Entirely, the atom has neutral characteristic because the sum of positive charges and equal to the sum negative charges.
c. During revolving the nucleus, the centripetal force on the electrons is formed from the attractive force among electrons and nucleus (Coulomb’s force)
Figure 2. Rutherford’s atomic model
D. Atomic Spectrum and Bohr’s Atomic Model
1. Continuous Spectrum
Light from many sources, such as the sun or light bulb appears white. If white light passes through a prism, it is separated into a spectrum with different colors. The prism separates the light by refracting or bending light of different colors at different angles. In this case, a white light consists of electromagnetic wave components with different in frequencies, wavelengths, and colors. Thus, spectrum is a distribution of colored light (monochromatic light) produced when a beam of white light (polychromatic light) is dispersed into its components. In other words, a given spectrum consists of a range of radiation frequencies of electromagnetic wave which has a specific property.
A spectrum emitted by a solid object heated to incandescence or by a liquid or a high dense gas is usually a continuous spectrum. In this case, the continuous spectrum is a sequence of electromagnetic wave frequencies that is without breaks over a relatively wide range of wavelengths.
In a continuous spectrum, the light of all colors is present in it and the colors blend continuously into one another and form a rainbow-like pattern. A continuous spectrum can be analyzed only by using spectrophotometric methods.
2. Line Spectrum
If a tube filled by a gas or vapor of a certain element such as lithium, barium, mercury, sodium, and neon, is conducted with a high-voltage electricity, atoms of the elements will emit electromagnetic wave (light) for several wavelengths. If this light is passes through a spectrometer and is analyzed, there will come up with a certain spectrum called the line spectrum. In this case, the line spectrum is a spectrum made of a series of distinct lines and this spectrum is a characteristic of emission or absorption by atoms.
3. Hydrogen Atom Spectrum
A light produced by hydrogen gas atoms can be analyzed by using a spectrometer and there is found that hydrogen atom spectrum is a line-spectrum (not continuous spectrum).
In 1885, J.J. Balmer discovered an empirical formula to explain the spectrum of hydrogen atom, that is as follows :
where :
λ = wavelength (m)
R = Rydberg’s constant (1,0974 x 107 m-1)
n = 3,4,5, …
The equation above is known as the Balmer’s series, and in this case, for n = 3 there is found wavelength of light is 656,3 nm, while for n = ~ there is found wavelength of light of 364,6 nm. Therefore, the wavelength of hydrogen spectrum is located in visible light region, that is between 364,6 nm to 656,3 nm.
Some time later, after Balmer had discovered the empirical formula for representing the wavelength of hydrogen spectrum, other scientists succeeded in formulating series which are similar to Balmer’s series, they are Lyman (1906), Paschen (1908), Bracket (1922), and Pfund (1924)
.
Lyman’s series } n = 2,3,4, …
Paschen’s series } n = 4,5,6, …
Bracket’s series } n = 5,6,7, …
Pfund’s series } n = 5,6,7, …If the wavelength of hydrogen spectrum according to Balmer’s series is located un the visible light region (Hδ = violet light, Hγ = blue light, Hβ = blue-green light, and Hα = red light), according to Lyman’s series, the wavelength is located in the ultraviolet region, and according to Paschen, Bracket, and Pfund series are located in the infra-red region.
4. Bohr’s Atomic Model
The weakness of Rutherford’s atomic theory in explaining the line spectrum of hydrogen atom was successfully corrected by Niels Bohr, in 1913, based on Rutherford’s atomic theory and Planck’s quantum theory, Bohr proposed postulates about atomic models, those are as follow :
- Electrons in atom revolve the nucleus at a certain path called stationary path. At this path, they do not absorb nor release energy and they have angular momentum, the magnitude of which is multiplication of
. - Electrons will release energy (in the form of photon) if they displace from a higher energy level to a lower one (from outer to the inner path) and electrons will absorb energy when they displace from a lower energy level to a higher one (from the inner to the outer space).
Figure 3. Bohr’s atomic model
Based on the Bohr’s postulates, several electron quantities in hydrogen atom such as velocity of electron in revolving the nucleus and energy of electron can be determined. From the Bohr’s first postulate, the angular momentum of electron complies the equation as follows :
where :
L = angular momentum of electron
m = mass of electron
v = velocity of electron
r = distance of electron to the nucleus
h = Planck’s constant
n = 1,2,3, …
By rearranging the equation of electron angular momentum, the linear velocity of electron in revolving the nucleus can be determined as follows :
Meanwhile, the total energy of electron in each orbit is as follows :
where :
En = energy of electron at n-th shell
These energy levels of electron can be diagrammatically depicted as follows :
Figure 4. Energy levels of electron
If an electron occupies the lowest energy level (n=1), the atom is said to be in the ground state. In the above diagram, the electron which is in the ground state is shown as Ο.
As an electron absorbs an amount of energy, which corresponds to the difference in energy between its present energy level and some other energy level, the electron will displace to a higher energy level (outer shell). The displacement of electron from the inner to the outer shell is called excitation, while the displacement of electron fro the excited state to the initial state is called transition. According to Bohr, in an excitation state, the electron absorbs energy, while in a transition state, the electron release energy. The energy absorbed or released by the electron is in the form of photon or light. The amount of energy absorbed or released by the electron at excitation or transition can be determined as follows :
Energy difference between the ground state (n = 1) and energy level where n = 2 is 10,2 eV. This amount of energy corresponds to energy which must be absorbed by the electron in order to “jump” from n = 1 to n = 2. Similarly, if the electron absorbs of 13.6 eV, the electron will displace to the energy level for n = 5.
Sample Problem 1.1.
An electron of hydrogen atom is in transition from the 2nd to the 1st shell, determine :
- the energy released
- the frequency of photon emitted
Solution
- the energy released
in Joule :
∆E = -10,2 x 1,6 x 10-19 Joule
= -1,63 x 10-18 Joule
Thus, the energy released by the electron is 10,2 eV or 1,63 x 10-18 Joule.
- the frequency of photon
∆E = hf
Thus, the frequency of photon is 2,45 x 1015 Hz.
The displacement of electrons in an atom from nth shell to the infinity shell will cause the atom to be charged (ionized) and the amount of energy required to release electrons from the nth shell to the infinity shell is called the ionization energy, which can be determined as follows :
E ionization = E final – E initial
= E ~ - En
= 
E. Quantum Mechanics Theory
Although the Bohr’s atomic theory can explain the phenomenon of hydrogen atom spectrum and it can be used to determine the electron quantities such as velocity and energy, it still has several weakness, among others are Bohr’s atomic model can only explain the hydrogen atom, while many electrons atoms cannot be explained using the Bohr’s atomic model ; the actual electron path is not so simple as proposed by Bohr (circular path), but it is more complicated and has the orbital subshells ; and the Bohr’s atomic theory cannot explain the occurrences in chemical bonds and the effect of magnetic field to an atomic spectrum.
Based on the above mentioned facts, the Bohr’s atomic theory was developed and corrected by other scientists and finally there obtained a modern atomic theory known as quantum mechanics theory. The followings are explanations about the quantum mechanics theory initiated by de Broglie wave and Heisenberg uncertainty principle.
1. de Broglie Wave
In 1923, Louis de Broglie proposed that all particles (not merely photon) have both wave and particle properties. de Broglie calculated that every particle has a wavelength which is equal to the Planck’s constant (h) divided by the momentum of particle (p).
In this case, λ is called de Broglie wavelength and any particles such as electrons and atoms have de Broglie wavelength. Because momentum of a certain particle depends on its speed and mass, the de Broglie wavelength of a particle can be formulated as follows :
where :
λ = wavelength of particle (m)
m = mass of particle (kg)
v = speed of particle (m/s)
de Broglie’s idea about the wave behavior possessed by a particle has successfully been proved by Davisson and Germer in 1927 through an experiment using electrons within a vacuum tube. In their experiment, Davisson and Germer accelerated electrons by using an electric field produced by an electric potential difference of V = 54 volt, so the electron have an amount of kinetic energy.
Although a particle can behave like a wave, the common objects do not show the behavior of wave, it is because the symptoms of a particle can occur if the particle has an extremely large in velocity (approaching the velocity of light). For example, a ball that moves with speed of 150 km/hour has wavelength about 1,1 x 10-34 m. The wavelength is not sufficient to make the ball behave like a wave.
2. Heisenberg Uncertainty Principle
The presence of particles behavior for light (electromagnetic wave) and wave behavior for the particles causes an uncertainty in measuring quantities, such as momentum and position of a particle. For example, the measurement of electron’s momentum using the instrument that involves light will resulting a measurement followed by the uncertainty. In fact, we cannot explain the motion of electrons based on the classical physic theories (Newtonian mechanics).
Based on the collision principle in classical mechanics consideration, in a collision between photon and electron there will be obtained measurement of momentum uncertainty which has value of at least equal to the momentum of photon, that is :
where :
∆ p = momentum of uncertainty
From the formulation above, the momentum of uncertainty of particle (electron) is inversely proportional to the wavelength of light (photon). The wavelength of light can be used to determine the value of the electron’s position uncertainty. The value of the electron’s position uncertainty is at least equal to the wavelength of light.
where :
∆ x = position uncertainty
The notation of and in the relation to momentum measurement has a meaning that, reducing the momentum uncertainty it can be done by increasing the wavelength of light and at the same time the position uncertainty will increase.
and in the relation to momentum measurement has a meaning that, reducing the momentum uncertainty it can be done by increasing the wavelength of light and at the same time the position uncertainty will increase. Based on the above case, in 1927, Warner Heisenberg formulated a principle known by Heisenberg uncertainty principle or indeterminacy principle. This principle plays role in the development of quantum mechanics.
In this case, the Heisenberg uncertainty principle prescribes that “It is impossible to measure or to specify the momentum and the position of a particle simultaneously with unlimited precision”. Or in other words “ the measurement of momentum and position of a particle simultaneously always results in an uncertainty which is never less than Planck’s constant”. Mathematically, Heisenberg uncertainty principle can be expressed in the following equation :
3. Schrodinger’s Wave Function
Based on de Broglie’s idea and Heisenberg uncertainty principle, in 1926 Erwin Schrodinger proposed an idea that if electrons have characteristics of wave, of course they have a wave function representing their state. According to Schrodinger, the wave function of electrons in revolving the nucleus of an atom can be represented by the free wave function of time as follows :
where :
A = wave amplitude
k = wave number
Because electrons have wave characteristics, according to Schrodinger, electrons in an atom do not orbit the nucleus, but they behave more likely as waves traveling at a certain distance with a given energy around the nucleus.
Schrodinger’s atomic model was proved to be more accurate and based on this model, physicists no longer try to find the electron’s path and its position in an atom. Instead, they use the equation describing the electron wave to find the region in which the electron is most likely to be found.
Based on the Schrodinger’s atomic model, the quantization of angular momentum of electron as it has been proposed by Bohr can occur because the electron wave forms a stationary wave. In this case, the atomic model based on wave characteristics of electron described by using this Schrodinger’s wave function is called the atomic model of quantum mechanics or atomic model of wave mechanics.
F. Quantum Numbers and Atomic Orbitals
The Bohr’s atomic model is a one-dimensional model using one quantum number to describe the distribution of electrons in an atom. Such information only relates to the size of the orbit of electrons in an atom, which was described by the n quantum number. Schrodinger’s atomic model allows electron to occupy three-dimensional space. Hence, to describe the orbitals in which electron can be found in an atom three coordinates or three quantum number are required.
The three coordinates or quantum numbers which come from the exact solution of Schrodinger’s wave equations are the principal quantum number (n), azimuth or angular quantum number (ℓ), and magnetic quantum number (m). Those quantum numbers describe the size, shape, and orientation of orbitals in an atom.
1. Principal Quantum Number (n)
Principal quantum number (n) describes the size of the orbital which refers to the quantum number n in the Bohr’s atomic theory. For example, orbital for which n = 2 is larger than that of for n = 1. The principal quantum number also indirectly describes the energy level of an orbital.
Based on Bohr’s atomic theory, the energy of electron in hydrogen atom (Z = 1) is 
, but for atoms besides hydrogen, the energy of electron obeys the equation as follows :
, but for atoms besides hydrogen, the energy of electron obeys the equation as follows :
Where :
Z = atomic number
n = principal quantum number (n = 1,2,3, …)
The position of electrons which appropriates to energy level of the electrons is represented by atomic shells and symbolized by K, L, M, N, O, P and so forth. The relation of the principal quantum number and the atomic shells is shown in the table below :
n | 1 | 2 | 3 | 4 | 5 | 6 |
Shell symbol | K | L | M | N | O | P |
2. Azimuth Quantum Number (ℓ)
Azimuth quantum number or angular quantum number is the number which represents the magnitude of angular momentum of electron and atomic subshell which determines atomic orbital shapes. The angular momentum of electron to the axis of atomic nucleus can be determined as follows :
In this case, ℓ is angular quantum number which has the values from zero to n – 1.
ℓ = 0, 1, 2, …, n-1
where :
n = principal quantum number
Each atomic subshell is symbolized by using letters of s, p, d, f, g, h, I, and so forth, which appropriates to the state of angular quantum number (ℓ). Pay attention to the following table :
ℓ | 0 | 1 | 2 | 3 | 4 | 5 | 6 | … |
Name of subshell | s | p | d | f | g | h | i | … |
The naming of subshell is based on the empirical classification of spectrum, suppose s from sharp, p from principal, d from diffuse, f from fundamental, and so forth.
3. Magnetic Quantum Number (m)
In physics, we have known that angular momentum is a vector quantity, so it has both a magnitude and direction.
If the magnitude of electron angular momentum is represented by angular quantum number, the direction or orientation of it is represented by the magnetic quantum number (m). Magnetic quantum number also represents a particular orbital occupied by electrons in a certain subshell. It is called the magnetic quantum number because the effect of different orientations of orbitals was initially observed in the presence of a magnetic field.
The value of magnetic quantum number depends on the value of angular quantum number, that is all integers begin from -ℓ to +ℓ, including zero.
m = -ℓ, …, 0, …, +ℓ
4. Atomic Orbitals
Atomic orbitals are mathematical descriptions of electron’s position in an atom which is most likely to be found. These descriptions are obtained by solving the Schrodinger’s equation. Each orbital has a size, shape, and orientation determined by the n, ℓ, m quantum numbers. The orbitals combine to form subshells and they can combine to form shells or energy levels.
Among the orbital shapes are spherical, polar, and cloverleaf shapes as shown in the following figure. The spherical shape occurs if ℓ = 0 ( s orbital) ; polar shape occurs if ℓ = 1 (p orbital) ; and cloveleaf shape occurs if ℓ = 2 (d orbital).
Figure 5. Orbital shapes for 
= 0, = 1, and = 2
= 0, = 1, and = 2 The orbitals above correspond to the three lowest energy states, those are s, p, and d respectively. The illustration in the figure 1.14 shows the spatial distribution of electrons within those orbitals. This description has been confirmed by many experiments in chemistry and physics, for example by using a Scanning tunneling Microscope.
In this case, orbital shapes can even take on more complex shapes as the value of angular quantum number becomes larger. Probability to find out electrons in s orbital (spherical shape) is same to any direction. However, for orbitals which have polar shape (p orbital) or cloverleaf (d orbital) can lead to different directions.
Orbitals having the same value of the principal quantum number from a shell. Orbitals within a shell are divided into subshells having the same value of angular quantum number. Chemist describe the shell and subshell in which an orbital belongs to a combination of principal quantum number (n) and angular quantum number (ℓ) is usually used to express the atomic state of electron symbolized by (n, ℓ). Where n indicates the shell, while ℓ indicates the subshell. For example, the orbital of the first shell (K) is represented by 1s (n = 1, ℓ = 0).
Moreover, the atomic state of electrons in an orbital can be represented by using the combination of three quantum numbers, those are principal, angular, and magnetic quantum numbers (n, ℓ, and m).
Based on the combination of those three quantum numbers, it is known that in n = 1shell three is only one orbital, that is 1s. It is because the s orbital has the spherical shape which is only possible to possess one orientation in a space. The only allowed combination of quantum numbers for which n = 1 is as follows.
n ℓ m
1 0 0 1s In n = 2 shell there are four orbitals. The allowed combination of quantum numbers for which n = 2 are as follows.
|
There is only one orbital in the 2s subshell and this orbital has the spherical shape which is bigger than is orbital. Meanwhile, there are three orbitals in the 2p subshell. It is because there are three directions in which a p orbital. One of these orbitals is oriented along the x axis, another along the y axis, and the third along the z axis in Cartesian coordinate system, as shown in the following figure. These orbitals are known as the 2px, 2py, and 2pz orbitals.
Figure 6. 1s, 2s and 2p orbitals
In n = 3 shell there are nine orbitals. The allowed combination of quantum numbers for n = 3 are as follows.
|
There is only one orbital in the 3s subshell and this orbital has the spherical shape which is bigger than 1s or 2s orbitals and there are three orbitals in 3p subshell. Meanwhile, there are five orbitals in the 3d subshell. It is because there are five directions in a d orbital. One of these is found on the xy plane of a Cartesian coordinate system and it is called the 3dxy orbital. Similar to that, there are the 3dxz and 3dyz orbitalswhich have the same shape, but they are found between the axes of the coordinate system on the xz and yz planes. The fourth orbital in this subshell lies along the x and y axes and it is called the 3dx2-y2 orbital and the fifth orbital lies along the z axis and this orbital is called the 3dz2 orbital. Consider the following figure.
Figure 7 . 3d orbitals
Based on the explanations about orbitals for n = 1, n = 2, and n = 3, the number of orbitals in a shell is the square of the principal quantum number (n2). Meanwhile, the number of orbitals in a subshell is 2(ℓ) + 1.
5. Spin Quantum Number (s)
Electrons in an atom are not only revolving he nucleus, but they are also rotating on their axis. The electron’s rotation on its axis is called spin and this state is represented by the spin quantum number (s).
The direction of an electron’s spin has only two possibilities, namely clockwise and counterclockwise directions. An electron which has a clockwise direction spin leads downward, while an electron which has a counterclockwise direction spin leads upward, it is shown in the following figure.
Figure 8. Electron’s spin
Because electron’s spin consists of two possibilities, the spin quantum number also has two values, those are 
(for upward spin) and 
(for downward spin).
(for upward spin) and (for downward spin). Based on the state of electron’s spin, accordingly each electron orbital is only occupied by two electrons. The two electrons must have opposite spins, so they produce an opposite magnetic field required to balance the repulsion force (Coulomb’s force) from these electrons in the orbital.
Exercise.
1. Calculate the number of subshell for n = 5 and determine the symbol of electron’s atomic state in the subshell of f in the shell and the magnitude of angular momentum.
2. What are the possible values of ℓ for n = 3 ?
3. What are the possible values of m for ℓ = 4, and determine the possible values of L and the number of orbitals.
4. Electron 1 has the quantum number combination of n = 3, ℓ = 2, and m = 2 while electron 2 has the quantum number combination of n = 3, ℓ = 1, and m = 0. Do these electrons have the same or different orbital ? Explain.
5. Determine the number of orbitals in the 4-th atomic shell and the number of orbitals in each subshell in the shell.
G. Electron Configuration
Electron configuration of an atom describes the distribution of electrons at the shells of an atom.
1. Aufbau Principle
Aufbau principle states that the filling of the electrons in an atom starts from the lowest energy orbital until all of the electrons which have been filled are in an appropriate orbital to the next higher energy orbital.
Because of the presence of attraction force between objects of opposite charge, the most important factor influencing the energy of an orbital is its size and the value of the principal quantum number, n. for an atom containing only one electron, there is no difference between the energies of the different subshells within a shell. For example, in a hydrogen atom, the 3s, 3p, and 3d orbitals have the same energy. However, for an atom containing more than one electron, the different subshells no longer have the same energy. Within a given shell, the s orbitals always have the lowest energy. In this case, the energy of the subshells gradually becomes larger as the value of the angular quantum number becomes larger.
The order of increasing energy for atomic orbitals can be written as follows :
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p < 8s…
2. Pauli Exclusion Principle
Electrons are a type of particle known as fermion. Wolfgang Pauli discovered that no fermions can have the exactly similar four quantum numbers. This principle is known as the Pauli exclusion principle, which states that two or more identical electrons cannot occupy the same orbital in an atom.
Each orbital in an atom can only hold two electrons. The two electrons in each orbital are differentiated by the electron’s spin or the spin quantum number. An electron’s spin has two possible values, namely (spin-up) and (spin-down). According to these two possible values of spin, it means that two electrons can occupy the same orbital, but their spins are different. Thus, two electrons in an orbital will form a pair which can be described as in the following figure.
(spin-up) and (spin-down). According to these two possible values of spin, it means that two electrons can occupy the same orbital, but their spins are different. Thus, two electrons in an orbital will form a pair which can be described as in the following figure.
|
Figure 9. An orbital diagram
Each subshell consists of a number of orbitals, and the maximum number of electrons in each subshell is equal to twice as much as the orbital number.
Table 1. The maximum number of electrons in each atomic subshell
Subshell | Orbital number | Maximum number of electrons |
s | 1 | 2 |
p | 3 | 6 |
d | 5 | 10 |
f | 7 | 14 |
3. Hund’s Rule
Electrons occupying the orbitals of an atom obey the rules are stated by Friedrich Hund. These rules are known as Hund’s rules which can be summarized as follows.
· One electron is added to each of the orbitals in a subshell before the second is added to any orbital in the subshell.
· Electrons are added to a subshell in the same value of the spin quantum number until each orbital in the subshell has at least one electron.
For C atom (Z = 6)
1s2 2s2 2p2
2px1 2py1 2pz0
| |
Figure 10. The filling of electrons in C atom according to Hund’s rule
For O atom (Z = 8)
1s2 2s2 2p2
2px2 2py1 2pz1
 | |  |
Figure 11. The filling of electrons in O atom according to Hund’s rule
The writing of electron configuration of a certain atom or ion must comply the Aufbau principle, Pauli exclusion principle, and Hund’s rule.
Table 2. Electron configuration for some atoms
Atom | The number of electrons | Electron configuration |
Hydrogen (H) | 1 | 1s1 |
Lithium (Li) | 3 | 1s2 2s1 |
Boron (B) | 5 | 1s2 2s2 2p1 |
Nitrogen (N) | 7 | 1s2 2s2 2p3 |
Fluorine (F) | 9 | 1s2 2s2 2p5 |
Sodium / Natrium (Na) | 11 | 1s2 2s2 2p6 3s1 |
Aluminum (Al) | 13 | 1s2 2s2 2p6 3s2 3p1 |
Potassium / Kalium (K) | 19 | 1s2 2s2 2p6 3s2 3p6 4s1 |
Scandium (Sc) | 21 | 1s2 2s2 2p6 3s2 3p6 4s2 3d1 |
Normally, the electron configuration of a certain atom can be abbreviated based on the electron configuration of noble gases atoms.
Ne configuration
Therefore, 
Table 3. The electron configuration of noble gases atoms
Atom | The number of electrons | Electron configuration |
Helium (He) | 2 | 1s2 |
Neon (Ne) | 10 | 1s2 2s2 2p6 |
Argon (Ar) | 18 | 1s2 2s2 2p6 3s2 3p6 |
Krypton (Kr) | 36 | 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 |
Xenon (Xe) | 54 | 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 |
Basically, the electron configuration of atoms obeys general rules, i.e., Aufbau principle, Pauli exclusion principle, and Hund’s rule. However, based on the result of spectrum observation for some atoms, in fact there is deviation to the general rules.
For example,
The electron configurations of atoms above are less stable, so they change to as follows.
According to examples above, in filling electrons, d subshell tend to be fully filled (10 electrons) or half-full (5 electrons). This condition is possible to happen because the (n-1)d and ns orbitals have a relatively small difference of energy level, so to reach the stable condition, the electron in the ns orbital can undergo an excitation to the (n-1)d orbital. In this case, if the (n-1)d orbital in an atom is fully filled or half-full by electrons, the atom is n a most stable condition.
4. Valence Electron
Valence electrons are electrons in the outermost shell of an atom. The valence electrons in an atom play a role in the formation of chemical bond. In the principal group elements, their valence electrons occupy the ns and np subshells, while in the transition group elements, their valence electrons occupy the (n-1)d and ns subshells.
(principal group)n = 2, then the valence electron of Ne atom is 8, from 2s subshell (2 electrons) and from 2p subshell (6 electrons).
(transition group)n = 4 and n-1 = 3, then the valence electron of Fe atom is 8, from 3d subshell (6 electrons) and from 4s subshell (2 electrons).
Exercise
1. What is the maximum number of electrons which can occupy a subshell the atomic state of which is represented by n = 3, 
= 2 ?
= 2 ?2. Calculate the maximum number of electrons found in M shell and denote the atomic state of the electron in each orbital.
3. Write down the electron configuration and orbital diagram for the following atoms.
a. 32Ge d. 40Zr
b. 52Te e. 48Cd
c. 56Ba f. 74W
H. Periodic Table
We have known that periodic table of elements is arranged based the properties resemblance of elements. The elements having similar properties are located in a group.
Figure 12. modern periodic table
Basically, the placement of elements in periodic table can be distinguished in a certain block. The placement of elements blocks in the periodic table relates to the electron configuration of the elements atom. Generally, the placement of elements blocks in periodic table can be described as follows
 |
Figure 13. The placement of elements blocks in periodic table
The placement of elements blocks in periodic table are relied on the valence electron configuration of elements atom. For elements in s blocks, the filling of electrons ends at s subshell, elements in p blocks, the filling of electrons ends at p subshell, elements in d blocks, the filling of electrons ends at dsubshell, elements in f blocks, the filling of electrons ends at f subshell.
Table 4. The valence electron configuration of elements in periodic table
Elements | Valence Electron Configuration | Block |
IA group | ns1 | s |
IIA group | ns1 | s |
IIIA group | ns2 np1 | p |
IVA group | ns2 np2 | p |
VA group | ns2 np3 | p |
VIA group | ns2 np4 | p |
VIIA group | ns2 np5 | p |
VIIIA group | ns2 np6 | p |
IB – VIIIB group | (n-1)dp nsq | d |
Lanthanide and Actinide series | (n-2)fp (n-1)d10 ns2 | f |
1. Determining Periods of Elements
Horizontal rows in periodic table correspond to the filling of electron in orbitals of a shell. For example, the second row consists of elements in which the orbitals are in the n = 2 shell. The following are electron configurations for element atoms in the second horizontal row of periodic table (second period).
Li (Z = 3) = [He] 2s1 O (Z = 8) = [He] 2s2 2p4
Be (Z = 4) = [He] 2s2 F (Z = 9) = [He] 2s2 2p5
C (Z = 6) = [He] 2s2 2p2 Ne (Z = 10) = [He] 2s2 2p6
N(Z = 7) = [He] 2s2 2p3
Based on the examples above, period of given element in periodic table can be determined based on its shell number indicated by the greatest value of the n (principal quantum number) in its electron configuration.
2. Determining Group of Elements
Elements in a group have similar configurations for their outer most electrons. This relationship can be seen at the electron configurations of elements as follows.
Group IA Group VIIA
He 1s1
Li [He] 2s1 Fe [He] 2s2 2p5
Na [Ne] 3s1 Cl [Ne] 3s2 3p5
K [Ar] 4s1 Br [Ar] 4s2 3d10 4p5
Rb [Kr] 5s1 I [Kr] 5s2 4d10 5p5
Cs [Xe] 6s1 At [Xe] 6s2 4f14 5d10 6p5
Based on the electron configuration of the elements above, the group of a given element in periodic table can be determined based on its valence number.
a. If electron configuration of an element atom ends at sx, the element is in xA group.
b. If electron configuration of an element atom ends at px, the element is in (x + 2)A group.
c. If electron configuration of an element atom ends at nsx (n-1)dy, the element is in group of :
· IIIB, if x + y = 3
· IVB, if x + y = 4
· VB, if x + y = 5
· VIB, if x + y = 6
· VIIB, if x + y = 7
· VIIIB, if x + y = 8, x + y = 9, x + y = 10
· IB, if x + y = 11
· IIB, if x + y = 12
d. If electron configuration of an element atom ends at fx, the element is in lanthanide and actinide groups.
3.Periodical Properties of Elements
1. Atomic Radius
Atomic radius is a distance between the nucleus of atom with the outermost atomic shell. Conception about the radius of atom was born because of the existing of assumption that atom is spherical in form.
a. In one group from the top downward, the atomic radius of the elements in periodic table are increasing.
b. In one group from the left rightward, the atomic radius of the elements in periodic table are decreasing.
The size (radius) of an atom is largely determined by its electrons. The electrons are arranged in shells surrounding the nucleus of each atom. The top elements of every group have only one or two electron shells. Atoms of elements further down the periodic table have more shells and therefore larger in size. In a period from left to the right, the atoms have same number of shells and the outermost electron (valance electron) fills up, but no shells are added more. At the same time, the number of protons in the nucleus of each atom are increases. Protons attract electrons. Greater the number of proton present, will make the attraction stronger which make the electrons closer to the nucleus, therefore the atom size will be smaller.
2. Ionization Energy
The amount of energy necessary to remove electrons from an atom is called the ionization energy. The ionization energy consists of many kinds, those are the first ionization energy, the second ionization energy, the third ionization energy, and so forth. The first ionization energy is energy required to remove an electron from the neutral atom, while the energy required to remove the next electron are named the second ionization energy, the third ionization energy, and so forth. The first ionization energy is always greater than the second ionization energy, and so forth.
a. In one period from the left rightward, the ionization energy of the elements in periodic table is greater, although there are the deviation on Na.
b. In one group from the top downward, the ionization energy of the elements in periodic table tend to decrease.
The increase of ionization energy of elements in one period from the left rightward happened because progressively rightward in one period, the atomic radius of elements is smaller, so the valence electrons of the atom attracted stronger to the nucleus and required a large energy to discharge the electron from the atom.
The decrease of ionization energy of elements in one group from the top downward is happened because progressively downward in one group, their atomic radius is greater, so the electrons on the outermost shell get the attractive force the nucleus which not too strong. Thus, required a little energy to discharge the electron from the atom.
3. Electron Affinity
Electron affinity is defined as an amount of energy used to remove an electron from a negatively charged or electron affinity is an energy used in the process of negative ion formation of the gas atom binding the electron from other atoms.
At one period from the left rightward in the periodic table the electron affinity is increasing, while at one group from the top downward the electron affinity of the elements in periodic table tend to decrease. Not all the electron affinity of the elements are positive in value, but there are any elements having negative value of electron affinity. The negative sign represent the releasing of energy process and the positive sign represent the absorption of energy process.
4. Electronegativity
Electronegativity is defined as a measure of how strongly an atom attracts electrons of the other atoms in their molecule. Beside that, electronegative is also defined as a measure tendency of atom in a molecule to attract the electrons in a chemical bond.
Electronegativity of an element is correlate with its ionization energy and electron affinity. In this case, mathematically the relationship of the three of them can be the equation as follows.
 |
where :
µ = electronegative
IA = ionization energy
Ei = electron affinity
Electronegativity of the elements in one period in the periodic table from the left rightward is increasing while for the one group elements from the top downward is decreasing.
Exercise
1. An element is in IVB group and fifth period. Determine :
a. electron configuration of the element
b. orbital diagram of the element atom
c. the number of unpaired electrons at the orbital
2. Determine the location of Rb, Mo, and I elements in periodic table if their atomic number are 37, 42, and 53 respectively.
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