Unit 2: Atomic Structure — Long Questions

Ans. Moseley's Law
Statement: This law states that "the square root of the frequency of the X-rays was directly proportional to the atomic number of an element".
Mathematical form: √frequency (v) ∝ Z

Explanation
In 1913, Moseley observed that when different elements were bombarded with cathode rays, the X-rays of some characteristics were produced.

Proton number He concluded that, the number of protons in the nucleus of an atom is called atomic number or proton number. It is represented by symbol 'Z' and it is fundamental property of an element.

Nucleon number The number of protons and neutrons in the nucleus of an atom is collectively called its nucleon number, also called mass number. It is represented by symbol 'A'. Atomic number is related to the mass number by the following equation.
A = Z + N

Example, an atom of an element X having atomic number Z and mass number A is described as ᶻX like ²⁷₁₃Al. Number of neutrons in an atom can be calculated as
N = A – Z

Consider ²⁷₁₃Al,
Atomic number/proton number (Z) = 13
Mass number/nucleon number (A) = 27
N = A – Z =27 – 13 = 14

Similarly, the number of electrons, protons and neutrons can be justified for an ion as in the following example:

²⁷₁₃Al atom loses three electrons to form Al³⁺, then;
Number of protons = 13
Number of neutrons = 14
Number of electrons = 13 – 3 = 10

Similarly, ³⁵₁₇Cl gain an electron to form Cl⁻ ion;
Number of protons = 17
Number of neutrons = 18
Number of electrons = 17 + 1 = 18

In case electron gain happens by the neutral atoms, say ¹⁶₈O to ₈O²⁻, ³¹₁₅P to ₁₅P³⁻ and ³²₁₆S to ₁₆S²⁻, the number of neutrons, protons and electrons are as follows.

Table 2.1 Number of protons, electrons and neutrons in different ions
Species Neutrons Protons Electrons
O²⁻ 8 8 10
S²⁻ 16 16 18
P³⁻ 16 15 18

Thus, the atomic number and proton number represent the same concept.

Ans. Fundamental Particles Electron, proton and neutron are said to be fundamental particles. The behaviour of particles in an electric field depends upon their mass and charge. If the beams of electrons, protons and neutrons are allowed to pass one by one at the same speed through an electric field, they show their behaviour as follows:

• Neutrons being neutral are not deflected but travel in a straight path perpendicular to the direction of electric field.
• Protons being positively charged are deflected towards the negative plate.
• Electrons being negatively charged are deflected towards the positive plate, to greater extent since they are 1/1836 times lighter than protons.

The amount of deviation from its original direction of movement is measured in two ways.

(i) Angle of deflection ∝ charge/mass
The angle of deflection of fundamental particles is directly proportional to the charge to mass ratio.

(ii) Radius of deflection ∝ mass/charge
The radius of deflection is directly proportional to mass to charge ratio.

Ans. Experimental Evidence The modern theory of electronic structure or atomic spectra originates from the Bohr Model of atom. Evidences for atomic models of the atoms derives principally from following two sources;
(i) Atomic spectra and ii) Ionization energies.

Atomic Spectra There are two types of atomic spectra.

(a) Atomic emission spectrum: When an element in its gaseous state is heated to high temperatures or subjected to electrical discharge, radiation of certain wavelengths is emitted. The spectrum of this radiation contains coloured lines and is called atomic emission spectrum. The atomic emission spectrum of hydrogen is shown in figure.

(b) Atomic Absorption Spectrum:
• When a beam of white light is passed through a gaseous sample of an element in cold state, certain wavelengths are absorbed.
• The wavelengths of the white light that has been absorbed by the atoms show up as dark lines on the spectrum.
• The spectrum of this radiation is called an atomic absorption spectrum.
• The atomic absorption spectrum of hydrogen is shown in figure.
• The wavelengths of the dark lines in the absorption spectrum are exactly the same as those of coloured lines in the emission spectrum.

Relation with electronic configuration

• Fixed energy levels: Each element has a unique arrangement of electrons and thus a unique range of fixed energy levels.
• Radiation: It follows the theory of the unique radiation. When electrons jump from one energy level to another must also be unique. This uniqueness convinces us to conclude that every element has its own characteristic spectrum.
• Identification of element: Every element is identified by its characteristic spectrum.
• Finger prints: We can say that atomic spectra are the finger prints of the elements. Figure shows the emission spectra of some elements.

Ans. Ionization and Energy levels
• A major difference between electrons in different types of shells is their energy.
• We can investigate the electronic configuration of the atoms by measuring experimentally the energies of the electrons within them.
• This can be done by measuring ionization energies of atoms.
Ionization energies are used to investigate the electronic configurations of elements in two ways.
(i) Successive ionization energies of the same element
(ii) First ionization energies for different elements

(i) Successive Ionization Energies of the Same Element
An atom of a particular element is studied and measure the energy required to remove each of its electrons, one by one.
X ⟶ X⁺ + e⁻ ΔHi₁
X⁺ ⟶ X²⁺ + e⁻ ΔHi₂
X²⁺ ⟶ X³⁺ + e⁻ ΔHi₃

Removal of electrons continuously from an atom until only the nucleus is left.
• We call this sequence of ionization energies, is successive ionization energies.
• The successive ionization energies show clearly the arrangement of electrons in shells around the nucleus.

Example If we take the magnesium atom as an example and measure the energy required to remove successively the first electron, the second, the third and so on.

• Graph: We obtain a graph when the ionization energies values are plotted against number of electrons as in figure.
• The plot shows that successive ionization energies increase when we move from the valence shell to the inner shell.
• First two electrons are removed from the outermost shell and require lower energy for their removal.
• A large increase occurs when the third electron is removed.
• This is because when two electrons of the outer shell have been removed, the next has to be removed from the shell that is very much closer to the nucleus.
• The next seven electrons are removed successively from the second shell and a gradual increase in ionization energy is observed.
• A similar but much more enormous jump occurs when the eleventh and twelfth electrons are removed from the first, innermost shell, right next to the nucleus.
• Conclusion: We observe two large jumps in the successive ionization energies. These two large jumps in the series of successive ionization energies are very good evidence that the electron in the magnesium atoms exist in three different shells.

(ii) First ionization energies of different atoms

Ionization energy and atomic No: The second way in which ionization energies show us the details of electronic configuration is to look at how the first ionization energies of elements vary with atomic numbers. The following figure shows a plot for the first 88 elements.
This graph tells us the following

(i) All ionization energies are strongly endothermic; it takes energy to separate an electron from an atom.

(ii) Decreases in Groups: As we go down a particular group, for example, from helium to neon to argon, or from lithium to sodium to potassium, ionization energies decrease.
• The larger the atom, the easier is to separate an electron from it.
• Reason: Actually, down the group, number of shells increases, hold of nucleus on the valence electrons decreases, hence removal of electrons becomes easier.

(iii) Increases in Period: The ionization energies generally increase on going across a period.
• The group 1 elements, the alkali metals, have the lowest ionization energy within each period and the noble gases have the highest.
• Reason: It is due to the reason that across the period shell number remains same. As the proton number increases, electrons are added in the same shell. Therefore, nucleus attracts the valence electrons more strongly. As a result, ionization energy increases across the period.

Ans. Definition Quantum numbers are set of numbers that describe the properties of atomic orbitals and the electron within them.

Quantum Numbers

Demerits of Bohr's Principal and Azimuthal model quantum number: The Bohr's model was a two-dimensional model that used one quantum number to describe the distribution of electrons in the atom.

• Merits of Bohr's model: The only important information was the size and energy of the orbit, which was described by the n-quantum number.
• Since Schrodinger's model allowed the electron to occupy three-dimensional space, therefore, it required three coordinates, or three quantum numbers, to describe the orbitals in which electrons can be found.
• The three quantum numbers that come from Schrodinger's wave equation are the principal (n), azimuthal (ℓ), and magnetic (m) quantum numbers.
• These quantum numbers describe the size, shape and orientation in space of the orbitals in an atom.

Principal Quantum number (n)
The principal quantum number, n, can have positive integral values 1,2,3,4... designated by K, L, M, N..., and it corresponds to the quantum number (number of orbit) in Bohr's model of the hydrogen atom.
• This quantum number, n, describes the size and energy of the orbital.
• The collection of orbitals with the same values of n is called an electron shell.
• The larger 'n' is, the greater the average distance of an electron in the orbital from the nucleus and therefore the larger the orbital.
• An increase in 'n' also means that the electron has a higher energy and is therefore less tightly bound to the nucleus.
• The principal Quantum number, n, can also be used to calculate the maximum number of electrons in a shell by the formula 2n². Therefore, shells K, L, M and N can accommodate maximum electrons 2,8,18,32 respectively.

Azimuthal Quantum Number (ℓ)

Definition • Azimuthal Quantum number, also called Angular Momentum Quantum Number, ℓ, can have integral values 0 to (n –1) for each value of n.

Explanation This quantum number describes the shape of the orbital.
• The number of subshells in a shell.
• The number of electrons in a subshell.

The values of 'ℓ' are integers that depend on the value of the principal quantum number.
If n = 1, there is only one possible value of 'ℓ' i.e. ℓ = 0 (n-1, where n = 1).
If n = 2, there are two values of 'ℓ' i.e. 0 and 1.
If n = 3 there are three values of 'ℓ' i.e., 0, 1 and 2.
If n = 4, there are four values of 'ℓ', i.e. 0,1,2 and 3.

• The values of 'ℓ' are designated by the letters s,p,d and f, with which stand for sharp, principle, diffused and fundamental, respectively.
• These are the spectral terms used to describe certain features of spectral lines.
• The set of orbitals that have the same n and ℓ values is called a subshell. The number of electrons in a subshell can be calculated by the formula 2(2ℓ+1) as given in the table 2.3.

Table 2.3 Shapes of orbital
Value of ℓ: 0, 1, 2, 3
Orbital designation: s, p, d, f
Shape of orbital: spherical, polar (dumb bell), cloverleaf (double dumbbell), complicated
No. of electrons in a subshell, 2(2ℓ+1): 2, 6, 10, 14

Table 2.4 Relationship between n, ℓ and subshells
Shell | Principal Quantum number 'n' | Azimuthal Quantum Number (ℓ) | Subshells | No. of subshells in a shell
K | 1 | 0 | 1s | 1
L | 2 | 0, 1 | 2s, 2p | 2
M | 3 | 0, 1, 2 | 3s, 3p, 3d | 3
N | 4 | 0, 1, 2, 3 | 4s, 4p, 4d, 4f | 4

Magnetic Quantum Number (m)

Definition The magnetic quantum number 'm' describes the orientation of an orbital in space.

Example Within a subshell, the value of m depends on the value of ℓ.
For a certain value of ℓ, there are (2ℓ + 1) integral values of m as follows: –ℓ......0......+ℓ.
• The values of m indicate the number of orbitals in a subshell.

If ℓ = 0, (s-subshell) there is only one possible value of m, i.e. 0. It means s-subshell has only 1 orbital.
If ℓ=1, (p-subshells) there are three values of m; -1,0 and +1. It means p-subshells have three orbitals.
If ℓ=2, (d-subshell), there are five values of m, namely, - 2, - 1, 0, + 1 and + 2. It means d-subshells have 5 orbitals.
If ℓ =3, (f-subshell) there are seven values of m: i.e. -3, -2, -1, 0, +1, +2, +3. It means f-subshells have 7 orbitals.

Orbitals of the same subshell have same energy and are called degenerate orbitals.
These degenerate orbitals are differentiated from each other in the presence of magnetic field, hence the name of this quantum number, i.e. magnetic quantum number. The relationship between the magnetic quantum numbers is provided in Table 2.5.

Table 2.5 Relationship between ℓ and m
Subshell | Azimuthal Quantum number (ℓ') | Magnetic Quantum number (m) | Number of degenerate orbitals (2ℓ+1)
s | 0 | 0 | One orbital
p | 1 | -1, 0, +1 | Three degenerate p-orbitals
d | 2 | -2, -1, 0, +1, +2 | Five degenerate d-orbitals
f | 3 | -3, -2, -1, 0, +1, +2, +3 | Seven degenerate f-orbitals

Spin Quantum Number (s)

Definition The spin quantum number describes the intrinsic angular moment of electron or its spin, whether it is clockwise or anticlockwise.

Electrons are thought of spinning around their own axes, as the Earth does.

According to electromagnetic theory, a spinning charge generates a magnetic field. It is the motion that causes an electron to behave like a magnet.

Figure shows the two possible spinning motions of an electron.

• One is clockwise and the other is anticlockwise. To take the electron spin into account, it is necessary to introduce a fourth quantum number called the electron spin quantum number (s).

Its values are + ½ and - ½, as in figure.

• The clockwise spin is represented by an arrow (↓) pointing downwards, while the anti-clockwise spin is represented by an arrow (↑) pointing upwards.

Each orbital can accommodate at the most two electrons provided the two have opposite spins.

Thus it takes three quantum numbers to describe an orbital but forth quantum number to differentiate between the two electrons that can occupy an orbital.

Ans. s-orbital The shape of an 's' orbital is spherical.

Explanation
• The electronic density around the nucleus in an 's' orbital is uniformly distributed in all directions.
• With the increase in the principal quantum number, the size of s orbital also becomes larger.

p-orbitals
The distribution of electron density for a 2p orbital is shown in figure.

Explanation
• The electron density is not distributed in a spherically symmetric fashion as in an s orbital.
• p orbital has two lobes on any of the axes.
• The p orbitals are named as px, py, and pz accordingly to their axis.

d-orbitals
In a given shell, 'd' orbitals have different shapes and orientations in space.

• Explanation: The dxy, dxz, and dyz lie in the xy, xz, and yz planes, respectively.
• The lobes of the dz² −y² lie along the x and y axes.
• The dz² orbital has two lobes along the z-axis and a "doughnut" in the xy plane.
• The shape of d orbital is complicated or sussage shape.
• The shapes for the five d orbitals (ℓ = 2,) are shown in Figure.

f-orbitals
An f subshell has seven orientations in space, i.e. there are seven f orbitals. However, the shapes of f orbitals are very complicated.

Ans. Definition Electronic configuration is the distribution of electrons among available shells, subshells, or orbitals of an atom or ion.

Example The configuration of 4 Be atom with two electrons in the '1s' subshell and two electrons in the '2s' subshell is written 1s²2s².

Explanation
• In case of subshells, the electronic configuration is described by a notation that lists the subshell symbols, one after the other.
• Each symbol has a superscript on the right. This gives the number of electrons in the subshell.
• Each group of orbitals in a subshell is labeled by its subshell notation. An electron in an orbital is shown by an arrow. The arrow points upward, when s = +½ and downward when s = −½. The orbital diagram of boron (5 B) is as follows.

5B = 1s¹¹ 2s¹¹ 2px 2p⁰y 2p⁰z

Distribution of electron in shells
The electronic configuration of an atom describes the distribution of electrons in its atomic shells. The shells, denoted as K, L, M, N, and so on, correspond to the principal quantum number (n) of the orbitals.

Shell capacities Each shell has a specific capacity for electrons:
K shell (n=1): 2 electrons maximum (1s orbital)
L shell (n=2): 8 electrons maximum (2s and 2p orbitals)
M shell (n=3): 18 electrons maximum (3s, 3p, and 3d orbitals)
N shell (n=4): 32 electrons maximum (4s, 4p, 4d, and 4f orbitals)

For example
Hydrogen (H): 1s¹ (K shell)
Helium (He): 1s² (K shell)
Sodium (Na): 1s² 2s² 2p⁶ 3s¹ (K L M)
2 8 1
Chlorine (Cl) = 1s² 2s² 2p⁶ 3s² 3p⁵ (K L M)
2 8 7

Distribution of Electrons in sub shells orbitals
In case of subshells, the electronic configuration is described by a notation that lists the subshell symbols, one after the other. Each symbol has a superscript on the right. This gives the number of electrons in the subshell.

Following rules are applied to fill the orbitals of multi-electron atoms.

Aufbau principle Aufbau principle is also known as the building up principle. This principle says that the subshells in an atom are filled with electrons in an increasing order of their energy values. Since, the energy of a subshell in the absence of any magnetic field, depends upon the principal quantum number (n) and the azimuthal quantum number (l).

n+l Rule: The order of filling subshells with electrons may be obtained from the summation (n + ℓ). values are given in Table.

Ans. Distribution of electrons in orbitals
A useful way of representing electronic configurations is a box diagram. Each box represents an orbital as shown in figure.
• Each box represents an atomic orbital.
• Each orbital con occupy maximum of two electrons.
• An electron is represented by an arrow.
• The boxes (orbitals) can be arranged in order of increasing energy from bottom to top.

The following rules are obeyed while filling orbitals with electrons.
Thus it takes three quantum numbers to describe an orbital but forth quantum number to differentiate between the two electrons that can occupy an orbital.

Pauli's Exclusion principle Statement: No two electrons in an atom can have the same values for all the four quantum numbers, or "Two electrons in an orbital will always have opposite spins".

Example In the first shell of helium (He) atom, there are two electrons. They are present in 1s orbital. According to the concept of quantum numbers and Pauli's exclusion principal, the values of their quantum numbers are:

Table 2.7 Values of quantum numbers of two electrons in the same orbital

Electron n ℓ m 's'
Electron 1 1 0 0 +1/2 (anti clockwise)
Electron 2 1 0 0 −1/2 (clockwise)

The two electrons having the same values of 'n', 'ℓ' and 'm' can have different values of 's'. It means that their spins are in the opposite directions.

Hund's rule
Statement: When degenerate orbitals are available and more than two electrons are to be placed in them, they should be placed in separate orbitals with the same spin rather than in the same orbital with opposite spins.

Example The three p-orbitals, i.e., px, py and pz have equal energy. To understand it, let us take an example in which three electrons are to be filled into three p-orbitals. There are two different ways to do this as shown below:

px py pz px py pz
↑↓ ↑ ↓ ↑ ↑ ↑
I (wrong) II (right)

According to Hund's rule 2ⁿᵈ one is right, configuration of p-orbital.

Explanation This rule gives an idea for filling electrons into the orbitals having equal energies.
According to the Hund's rule, the correct way of filling three electrons in three p orbitals is in which each orbital is singly occupied.

Electronic configuration in terms of orbitals in carbon, nitrogen, oxygen is provided in figure.

Ans. The arrangement in group
The electronic configurations of elements are related to their position in the periodic table. The periodic table is structured so that elements with the same pattern of outer-shell (valence) electronic configuration are arranged in same groups.

Location of Elements
You can easily write the electronic configuration of an element based on its location in the periodic table. Notice that in the periodic table the elements can be grouped in terms of the type of orbital into which the electrons are placed.

s-Block elements
• On the left are two columns of elements.
• These elements, known as the alkali metals and alkaline earth metals (groups 1 and 2),
• Those in which the outer-shell s orbitals are being filled.
• The group 1 and 2 elements all have ns¹ and ns² outer configurations respectively.

p-Block elements
• When we jump to group 13 elements, we find that they have ns²np¹ configuration.
• On the right is a block of six columns.
• These are the elements in which the outermost 'p' orbitals are being filled.

Transition elements (d & f-block elements):
• In the middle of the table is a block of ten columns that contain the transition metals.
• In these, the d orbitals are being filled.
• Below the main portion of the table are two rows that contain fourteen columns.
• These elements are often referred to as the f-block elements. These are the ones in which the 'f' orbitals are being filled.
• Recall that the numbers 2, 6, 10, and 14 are precisely the number of electrons that can fill the s, p, d, and f subshells, respectively.

Ans. Valence electrons
Definition: The electrons in an atom in the outermost shell are called valence electrons.

Explanation These are such electrons that are primarily involved in chemical reactions. The similarities among the configurations of valence electrons account for similarities of the chemical properties among groups of elements.

Figure shows a periodic table which include the valence shell configurations. Note the similarity in electron configuration within any group (column) of elements.

Classification of elements in periodic table
• The main-group or representative elements all have valence-shell configurations ns np^b.
• They have some choice of 'a' and 'b'.
• In other words, the outer 's' or 'p' subshell is being filled.
• In the d-block transition elements, a 'd' subshell is being filled.
• In the f-block transition elements or inner-transition elements, an 'f' subshell is being filled.
• There is a definite pattern to the order of filling of the subshells as we go through the elements in the periodic table.
• From this we can write down the building-up order.

The overall sketch of periodic table is given in figure, shows the blocks of elements.

Ans. Electronic configuration of ions

Positive ions Positive ions are formed when electrons are removed from atoms. The sodium ion, Na⁺ (proton number = 11), has 10 electrons. So, its electronic configuration is 1s² 2s² 2p⁶.
Note that this is the same as the electronic configuration of neon, the element with 10 electrons in each atom.

Negative ions Negative ions are formed when atoms gain electrons. The sulfide ion, S²− (proton number = 16), has 18 electrons. Its electronic configuration is 1s² 2s² 2p⁶ 3s² 3p⁶, which is the same as argon, the element with 18 electrons in each atom.

Ions of transition elements In general, electrons in the outer subshell are removed when metal atoms form the positive ions. However, the d-block elements behave slightly differently. Reading across the periodic table from potassium to zinc, the 4s subshell fills before the 3d subshell. But when atoms of a d-block element lose electrons to form ions, the 4s electrons are lost first.

Examples
Ti: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d² 4s²
Ti²⁺ ion: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d²

Cr atom 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁵ 4s¹
Cr³⁺ ion: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d³

Free radicals

Definition "A free radical is a specie that has one or more unpaired electrons".

An example of a simple free radical is free chlorine atom :Ċl: The electronic configuration of this radical is 1s² 2s² 2p⁶ 3s² 3p⁵. In the 3p-subshell, two orbitals have paired electrons whereas, the third one contains a single unpaired electron. The unpaired electron is shown by a single dot as in Cl•. Apart from single atoms, group of atoms can also be free radicals.

Example Some of free radicals are OH• , CH₃• etc.

Ans. Semiconductors
Semiconductors are materials that can conduct electricity under some conditions. They are used in many electronic devices, including smartphones, laptops, and cars.

Example The elements that can act as semiconductors are silicon, germanium and arsenic etc. The formation of semiconductors is possible because of a unique electronic configuration of these elements. Consider the example of Si and explore how it can be converted into a p-type and n-type semiconductors.

Silicon as non-semiconductor The electron configuration of 14Si = 2, 8, 4; meaning that it has 4 electrons in its valence shell. In the pure crystalline form, each Si atom bonded to four other Si atoms. In this form, there is no possibility of electronic conduction through the Si crystal.

P-type and N-type semiconductors are formed by "doping" a pure semiconductor material with impurity atoms, where adding trivalent impurities (like boron or aluminum) creates a P-type semiconductor, while adding pentavalent impurities (like phosphorus or arsenic) creates an N-type semiconductor. The difference lies in whether the added impurity creates "holes" (positive charge carriers) in the lattice, leading to P-type, or extra electrons (negative charge carriers) leading to N-type.

P-type semiconductor formation
Impurity atoms with three valence electrons (like Aℓ) are added to the pure semiconductor. Some of the trivalent atoms take place of the Si atoms in the crystals. The silicon atoms cannot make four bonds due to the lack of electrons. For this reason, there are created holes in the crystal lattice, which act as positive charge carriers as shown in figure. This process creates a positive-type semiconductor or P-type semiconductor. Electrons from an external current source can move through the semiconductor and it can act as a conductor.

N-type semiconductor formation When impurity atoms with five valence electrons (like phosphorus) are added to the pure semiconductor, some of Si atoms are replaced with the pentavalent phosphorus atoms. The Si atoms in the vicinity of these atoms can make four bonds and the fifth electron is an extra electron. These impurity atoms contribute extra electrons to the crystal lattice, which become free to move and act as negative charge carriers as in figure. The result is an N-type semiconductor that can conduct electricity when connected to an external source.