The Periodic Table is considered a cornerstone concept in chemistry. It provides a structured framework for organising the chemical elements, revealing patterns and trends in their properties, which is invaluable for both learning and research. It demonstrates that the elements are not a random collection but exhibit relationships and form families based on their characteristics.

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Why Do We Need To Classify Elements ?

Elements are the fundamental building blocks of all matter. In the early 19th century (around 1800), only about 31 elements were known. By the mid-19th century (1865), this number had doubled to 63. Currently, over 118 elements have been identified, with many of the heavier ones being synthesised artificially. Studying the chemistry of each element and the vast number of compounds they form individually is incredibly challenging.

To manage this complexity, scientists sought a systematic method to classify elements based on their properties. Such classification would not only help organise existing knowledge about elements but also potentially predict the properties of new or undiscovered ones, guiding further research.

Genesis Of Periodic Classification

The development of the Periodic Table was a gradual process, built upon the efforts of many scientists who observed and systematised the properties of known elements.

• In the early 1800s, German chemist Johann Dobereiner noticed similarities in the properties of certain groups of three elements, which he called Triads. He observed that the atomic weight of the middle element in a triad was often approximately the average of the atomic weights of the other two, and its properties were intermediate.

Element	Atomic weight	Element	Atomic weight	Element	Atomic weight
Li	7	Ca	40	Cl	35.5
Na	23	Sr	88	Br	80
K	39	Ba	137	I	127

However, this "Law of Triads" only worked for a limited number of elements and was not universally accepted.

• In 1862, French geologist A.E.B. de Chancourtois arranged elements by increasing atomic weight on a cylinder (the 'telluric helix'). He noted a periodic recurrence of properties, but his work didn't gain widespread attention.
• In 1865, English chemist John Alexander Newlands proposed the Law of Octaves. He arranged elements in increasing order of atomic weight and observed that the properties of every eighth element were similar to the first, like notes in a musical octave.

Element	Li	Be	B	C	N	O	F
At. wt.	7	9	11	12	14	16	19
Element	Na	Mg	Al	Si	P	S	Cl
At. wt.	23	24	27	29	31	32	35.5
Element	K	Ca
At. wt.	39	40

Newlands' law worked reasonably well only for the lighter elements, up to calcium, and wasn't accepted by the scientific community at the time, although he was later recognised for his contribution.

The most significant steps towards the modern Periodic Table were taken by Russian chemist Dmitri Mendeleev and German chemist Lothar Meyer, working independently around 1869. Both found that when elements were arranged by increasing atomic weight, similar physical and chemical properties recurred periodically. Lothar Meyer plotted properties like atomic volume and melting point against atomic weight, showing periodic patterns and noticing variations in the length of these repeating periods. His table from 1868 closely resembled the modern one but was published after Mendeleev's work.

Mendeleev is widely credited with publishing the first clear statement of the Periodic Law:

The properties of the elements are a periodic function of their atomic weights.

Mendeleev arranged elements in rows (periods) and columns (groups) based on increasing atomic weight, placing elements with similar properties in the same vertical column. He used a broader range of properties than Meyer, including the formulas of oxides and hydrides, recognising the fundamental importance of periodicity.

Crucially, Mendeleev did not strictly adhere to the increasing order of atomic weight when it contradicted the placement based on chemical properties. He believed the atomic weight measurements might be inaccurate (which was true in some cases, like for Iodine and Tellurium). He also bravely left gaps in his table, predicting the existence and properties of undiscovered elements that would fit into those positions. For example, he predicted elements he called Eka-Aluminium and Eka-Silicon, later discovered as Gallium and Germanium, whose properties closely matched his predictions.

Property	Eka-aluminium (predicted)	Gallium (found)	Eka-silicon (predicted)	Germanium (found)
Atomic weight	68	70	72	72.6
Density / (g/cm$^3$)	5.9	5.94	5.5	5.36
Melting point /K	Low	302.93	High	1231
Formula of oxide	E$_2$O$_3$	Ga$_2$O$_3$	EO$_2$	GeO$_2$
Formula of chloride	ECl$_3$	GaCl$_3$	ECl$_4$	GeCl$_4$

Mendeleev's successful predictions solidified the importance of his Periodic Table.

Modern Periodic Law And The Present Form Of The Periodic Table

At the time of Mendeleev, the internal structure of atoms was unknown. Developments in the early 20th century, particularly by English physicist Henry Moseley in 1913, provided a more fundamental basis for the periodic classification. Moseley studied the characteristic X-ray spectra of elements and found that the square root of the frequency of emitted X-rays ($\sqrt{\nu}$) plotted against the atomic number ($Z$) yielded a straight line, whereas a plot against atomic mass did not. This showed that the atomic number is a more fundamental property of an element than its atomic mass.

This led to the refinement of the Periodic Law, now known as the Modern Periodic Law:

The physical and chemical properties of the elements are periodic functions of their atomic numbers.

The atomic number ($Z$) represents the number of protons in the nucleus and also the number of electrons in a neutral atom. Since chemical properties are determined primarily by the electronic configuration, the periodic variation in properties is a direct consequence of the periodic variation in electronic configurations as atomic number increases.

The most widely used form today is the "long form" of the Periodic Table. It organises elements in horizontal rows called periods and vertical columns called groups. Elements in the same group have similar outer electronic configurations and hence similar properties.

According to IUPAC recommendations, groups are numbered 1 through 18, replacing older notations like IA-VIIA, VIII, IB-VIIB, and 0.

There are seven periods. The period number corresponds to the highest principal quantum number ($n$) of the valence shell being filled in that period. The number of elements in each period corresponds to the electron capacity of the orbitals being filled:

• Period 1 ($n=1$): Fills 1s (1 orbital). Maximum 2 electrons. 2 elements (H, He).
• Period 2 ($n=2$): Fills 2s, 2p (1+3=4 orbitals). Maximum 8 electrons. 8 elements (Li to Ne).
• Period 3 ($n=3$): Fills 3s, 3p (1+3=4 orbitals). Maximum 8 electrons. 8 elements (Na to Ar).
• Period 4 ($n=4$): Fills 4s, 3d, 4p (1+5+3=9 orbitals). Maximum 18 electrons. 18 elements (K to Kr). (Note the filling order 4s before 3d).
• Period 5 ($n=5$): Fills 5s, 4d, 5p (1+5+3=9 orbitals). Maximum 18 electrons. 18 elements (Rb to Xe). (Note the filling order 5s before 4d).
• Period 6 ($n=6$): Fills 6s, 4f, 5d, 6p (1+7+5+3=16 orbitals). Maximum 32 electrons. 32 elements (Cs to Rn). The 14 elements filling the 4f orbitals (Lanthanoids) are placed separately below the main table.
• Period 7 ($n=7$): Fills 7s, 5f, 6d, 7p (1+7+5+3=16 orbitals). Maximum 32 electrons. This period is incomplete but contains 32 elements discovered so far, including the Actinoids (filling 5f orbitals), placed separately below the main table.

Lanthanoids and Actinoids are placed in separate panels at the bottom to keep the main body of the Periodic Table manageable and to group elements with very similar properties (within each series) together.

Nomenclature Of Elements With Atomic Numbers > 100

Traditionally, the discoverers of a new element had the privilege of naming it, which was then ratified by IUPAC. However, for elements with atomic numbers greater than 100, synthesised in different labs, competing claims for discovery led to disputes over naming (e.g., element 104 claimed by both American and Soviet scientists). To avoid this, IUPAC established a systematic temporary nomenclature for elements before their discovery is fully verified and a permanent name is agreed upon.

The temporary name is derived directly from the atomic number using numerical roots (Table 3.4) and adding the ending "-ium". The roots are combined in the order of the digits in the atomic number.

Digit	Name	Abbreviation
0	nil	n
1	un	u
2	bi	b
3	tri	t
4	quad	q
5	pent	p
6	hex	h
7	sept	s
8	oct	o
9	enn	e

The temporary symbol is derived from the abbreviations of the roots, using the first letter of each root.

Examples of IUPAC temporary names and symbols for elements with Z > 100 (Table 3.5 shows both temporary and official names):

Atomic Number	Name according to IUPAC nomenclature	Symbol according to IUPAC nomenclature
101	Unnilunium	Unu
104	Unnilquadium	Unq
118	Ununoctium	Uuo

Once the discovery is verified, a permanent name and one- or two-letter symbol are assigned, often honouring a scientist or place of discovery. Official names have been announced for all elements up to Z=118 (Oganesson).

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Answer:

Electronic Configurations Of Elements And The Periodic Table

The arrangement of elements in the modern Periodic Table is fundamentally based on their electronic configurations, specifically the quantum numbers of the last electron added to an atom.

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(a) Electronic Configurations in Periods

Each period in the Periodic Table corresponds to the filling of electrons into the orbitals of a new principal energy level (shell), indicated by the principal quantum number ($n$) which matches the period number. The number of elements in each period is determined by the total number of electrons that can fill the subshells available in that principal energy level, following the Aufbau principle's energy ordering.

• Period 1 ($n=1$): Fills the 1s orbital. The maximum capacity of the 1s orbital is 2 electrons. Thus, Period 1 has 2 elements (H: $1s^1$, He: $1s^2$).
• Period 2 ($n=2$): Starts filling the 2s orbital, then the 2p orbitals. Orbitals available are 2s (1 orbital) and 2p (3 orbitals). Total orbitals = 4. Maximum capacity = $4 \times 2 = 8$ electrons. Thus, Period 2 has 8 elements (Li: $[He]2s^1$ to Ne: $[He]2s^22p^6$).
• Period 3 ($n=3$): Starts filling the 3s orbital, then the 3p orbitals. Orbitals available are 3s (1 orbital) and 3p (3 orbitals). Total orbitals = 4. Maximum capacity = $4 \times 2 = 8$ electrons. Thus, Period 3 has 8 elements (Na: $[Ne]3s^1$ to Ar: $[Ne]3s^23p^6$).
• Period 4 ($n=4$): Fills 4s, then 3d, then 4p orbitals. Orbitals filled are 4s (1 orbital), 3d (5 orbitals), and 4p (3 orbitals). Total orbitals = $1+5+3=9$. Maximum capacity = $9 \times 2 = 18$ electrons. Thus, Period 4 has 18 elements (K: $[Ar]4s^1$ to Kr: $[Ar]3d^{10}4p^6$). The filling of 3d orbitals starts from Scandium ($Z=21$) and forms the first transition series.
• Period 5 ($n=5$): Fills 5s, then 4d, then 5p orbitals. Orbitals filled are 5s (1 orbital), 4d (5 orbitals), and 5p (3 orbitals). Total orbitals = $1+5+3=9$. Maximum capacity = $9 \times 2 = 18$ electrons. Thus, Period 5 has 18 elements (Rb: $[Kr]5s^1$ to Xe: $[Kr]4d^{10}5p^6$). The filling of 4d orbitals starts from Yttrium ($Z=39$) and forms the second transition series.
• Period 6 ($n=6$): Fills 6s, then 4f, then 5d, then 6p orbitals. Orbitals filled are 6s (1 orbital), 4f (7 orbitals), 5d (5 orbitals), and 6p (3 orbitals). Total orbitals = $1+7+5+3=16$. Maximum capacity = $16 \times 2 = 32$ electrons. Thus, Period 6 has 32 elements (Cs: $[Xe]6s^1$ to Rn: $[Xe]4f^{14}5d^{10}6p^6$). The filling of 4f orbitals starts from Cerium ($Z=58$) and forms the Lanthanoid series, placed separately.
• Period 7 ($n=7$): Fills 7s, then 5f, then 6d, then 7p orbitals. Orbitals available are 7s (1 orbital), 5f (7 orbitals), 6d (5 orbitals), and 7p (3 orbitals). Total orbitals = $1+7+5+3=16$. Maximum capacity = $16 \times 2 = 32$ electrons. This period includes elements up to $Z=118$. The filling of 5f orbitals starts after Actinium ($Z=89$) and forms the Actinoid series, placed separately.

The placement of Lanthanoids and Actinoids separately is a matter of convenience to keep the main table's width manageable and group elements with very similar properties within their respective series.

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Answer:

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(b) Groupwise Electronic Configurations

Elements within the same vertical column (group) in the Periodic Table share similar chemical properties. This similarity is because they have the same number and distribution of electrons in their outermost (valence) shell orbitals. The general valence shell electronic configuration is the same for all elements in a group.

For example, all Group 1 elements (Alkali Metals) have a valence shell electronic configuration of $ns^1$, where $n$ is the period number:

• Li ($Z=3$): $[He]2s^1$ ($n=2$)
• Na ($Z=11$): $[Ne]3s^1$ ($n=3$)
• K ($Z=19$): $[Ar]4s^1$ ($n=4$)
• Rb ($Z=37$): $[Kr]5s^1$ ($n=5$)
• Cs ($Z=55$): $[Xe]6s^1$ ($n=6$)
• Fr ($Z=87$): $[Rn]7s^1$ ($n=7$)

This consistent outer electronic configuration is the fundamental reason behind the similar chemical behavior within a group. While electronic configuration explains periodicity based on atomic number, chemical properties are the observable manifestation of these electron arrangements.

Electronic Configurations And Types Of Elements: S-, P-, D-, F- Blocks

Based on which subshell the last electron enters, elements in the Periodic Table are classified into four blocks: s-block, p-block, d-block, and f-block. This classification is directly linked to the electronic configurations and largely dictates the chemical behavior of the elements.

There are two notable exceptions to this simple block categorisation:

• Helium (He, $Z=2$): Has the configuration $1s^2$. While it technically belongs to the s-block, its properties are very similar to other noble gases (Group 18) due to its completely filled valence shell. Therefore, it's placed in the p-block.
• Hydrogen (H, $Z=1$): Has the configuration $1s^1$. It shares properties with Group 1 (alkali metals) due to having one valence electron, but also with Group 17 (halogens) because it can gain an electron to achieve a stable configuration ($1s^2$). Its chemistry is unique, and it's often placed separately at the top of the Periodic Table.

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The S-Block Elements

These are the elements of Group 1 (Alkali Metals) and Group 2 (Alkaline Earth Metals). The last electron enters the outermost s orbital.

• General outer electronic configuration: $ns^1$ (Group 1) and $ns^2$ (Group 2).
• They are all reactive metals.
• They have low ionisation enthalpies (energy required to remove an electron).
• They readily lose their valence electron(s) to form cations: $1^+$ ions (Group 1) and $2^+$ ions (Group 2).
• Their metallic character and reactivity generally increase down the group.
• Due to high reactivity, they are never found in elemental form in nature, only in compounds.
• Their compounds are predominantly ionic, except for some compounds of Lithium (Li) and Beryllium (Be) which show more covalent character due to their small size and high charge density.

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The P-Block Elements

These elements are located on the right side of the Periodic Table, from Group 13 to Group 18. The last electron enters the outermost p orbital. The s-block and p-block elements collectively are called Representative Elements or Main Group Elements.

• General outer electronic configuration: $ns^2np^{1-6}$ in each period.
• The number of electrons in the p subshell increases from 1 in Group 13 ($ns^2np^1$) to 6 in Group 18 ($ns^2np^6$).
• Group 18 elements are the Noble Gases, having a completely filled valence shell ($ns^2np^6$), which is a very stable configuration. This results in very low chemical reactivity.
• Preceding the noble gases are the Halogens (Group 17, $ns^2np^5$) and the Chalcogens (Group 16, $ns^2np^4$). These are important groups of non-metals.
• Halogens and Chalcogens have highly negative electron gain enthalpies (energy released when gaining an electron) and readily gain 1 or 2 electrons, respectively, to achieve the stable noble gas configuration.
• The non-metallic character increases as you move from left to right across a period in the p-block.
• The metallic character increases as you go down a group in the p-block.

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The D-Block Elements (Transition Elements)

These elements are located in the middle of the Periodic Table, from Group 3 to Group 12. They are characterised by the filling of the inner d orbitals, specifically $(n-1)d$ orbitals, before the outermost $ns$ orbital is completely filled.

• General outer electronic configuration: $(n-1)d^{1-10}ns^{0-2}$. (Some exceptions exist, like Cr and Cu).
• They are all metals.
• They typically form coloured ions in solution.
• They exhibit variable valency or oxidation states.
• Many are paramagnetic (attracted to a magnetic field) due to unpaired electrons in d orbitals.
• Many d-block elements and their compounds are used as catalysts.
• Elements in Group 12 (Zn, Cd, Hg) have $(n-1)d^{10}ns^2$ configuration. Since their d subshells are completely filled in both their elemental state and common oxidation states ($Zn^{2+}, Cd^{2+}, Hg^{2+}$), they do not exhibit most of the characteristic properties of transition elements. They are often considered post-transition metals or sometimes included as transition elements based on the definition of a 'd-block element'.
• Transition metals act as a bridge between the highly reactive s-block metals and the less reactive p-block elements (Groups 13-14), hence their name "Transition Elements".

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The F-Block Elements (Inner-Transition Elements)

These elements form two separate rows placed below the main body of the Periodic Table.

• The first series is the Lanthanoids (Ce, $Z=58$ to Lu, $Z=71$), filling the 4f orbitals.
• The second series is the Actinoids (Th, $Z=90$ to Lr, $Z=103$), filling the 5f orbitals.
• They are characterised by the filling of the inner f orbitals, specifically $(n-2)f$ orbitals, before the $(n-1)d$ or $ns$ orbitals are completely filled.
• General outer electronic configuration: $(n-2)f^{1-14}(n-1)d^{0-1}ns^2$.
• They are all metals.
• Elements within each series (especially the Lanthanoids) exhibit very similar properties because the f orbitals are deep inside the atom and screen the outer electrons from the increasing nuclear charge effectively, leading to only a small change in size (Lanthanoid contraction and Actinoid contraction).
• The chemistry of Actinoids is more complex than Lanthanoids due to a wider range of accessible oxidation states.
• All Actinoid elements are radioactive.
• Many Actinoids are synthesised artificially in very small quantities. Elements with $Z > 92$ (Uranium) are called Transuranium Elements.

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Problem 3.3. The elements Z = 117 and 120 have not yet been discovered. In which family / group would you place these elements and also give the electronic configuration in each case.

Answer:

To determine the group and electronic configuration, we need to consider the period and the block where the last electron would enter, based on the Aufbau principle.

We can extend the filling order: $1s \rightarrow 2s \rightarrow 2p \rightarrow 3s \rightarrow 3p \rightarrow 4s \rightarrow 3d \rightarrow 4p \rightarrow 5s \rightarrow 4d \rightarrow 5p \rightarrow 6s \rightarrow 4f \rightarrow 5d \rightarrow 6p \rightarrow 7s \rightarrow 5f \rightarrow 6d \rightarrow 7p \rightarrow 8s \dots$

Let's find the electronic configuration by filling electrons according to this order up to the given atomic numbers.

Noble gas configurations are useful here:

• [He] ($Z=2$): $1s^2$
• [Ne] ($Z=10$): $[He]2s^22p^6$
• [Ar] ($Z=18$): $[Ne]3s^23p^6$
• [Kr] ($Z=36$): $[Ar]4s^23d^{10}4p^6$
• [Xe] ($Z=54$): $[Kr]5s^24d^{10}5p^6$
• [Rn] ($Z=86$): $[Xe]6s^24f^{14}5d^{10}6p^6$
• [Uuo] ($Z=118$): $[Rn]7s^25f^{14}6d^{10}7p^6$

Element with Z = 117:

This element is just before the noble gas Uuo ($Z=118$). The last electron would be the 7th electron added to the 7p subshell (since 7p can hold up to 6 electrons). Elements with the configuration $ns^2np^5$ belong to Group 17 (Halogen family).

The configuration up to $Z=118$ is $[Rn]7s^25f^{14}6d^{10}7p^6$. To get $Z=117$, we remove one electron from the last filled subshell, which is 7p.

Electronic configuration of $Z=117$: $[Rn]7s^25f^{14}6d^{10}7p^5$.

This outer configuration ($7s^27p^5$) is similar to other Group 17 elements ($ns^2np^5$).

Therefore, the element with $Z=117$ would belong to the Halogen family (Group 17).

Element with Z = 120:

This element is two atomic numbers after Uuo ($Z=118$). After the 7p subshell is filled at $Z=118$, the next orbitals to be filled are 8s (according to the Aufbau principle/$(n+l)$ rule, $8+0=8$, while 7d is $7+2=9$). The first two electrons after $Z=118$ would go into the 8s orbital.

Electronic configuration of $Z=118$: $[Rn]7s^25f^{14}6d^{10}7p^6$.

Electronic configuration of $Z=119$: $[Rn]7s^25f^{14}6d^{10}7p^68s^1$ or $[Uuo]8s^1$. This would be in Group 1.

Electronic configuration of $Z=120$: $[Rn]7s^25f^{14}6d^{10}7p^68s^2$ or $[Uuo]8s^2$. This outer configuration ($8s^2$) is similar to other Group 2 elements ($ns^2$).

Therefore, the element with $Z=120$ would be placed in Group 2 (Alkaline Earth Metals).

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Metals, Non-Metals And Metalloids

Elements can also be broadly classified based on their physical and chemical properties into Metals, Non-metals, and Metalloids.

• Metals:
  • Comprise over 78% of all known elements.
  • Located on the left side of the Periodic Table.
  • Usually solid at room temperature (except Mercury, which is liquid; Gallium and Caesium have low melting points).
  • Generally have high melting and boiling points.
  • Are good conductors of heat and electricity.
  • Are malleable (can be hammered into thin sheets).
  • Are ductile (can be drawn into wires).
  • Metallic character generally increases down a group and decreases across a period from left to right.
• Non-metals:
  • Located on the top right-hand side of the Periodic Table.
  • Are usually solids or gases at room temperature (Bromine is the only liquid non-metal).
  • Generally have low melting and boiling points (exceptions include Boron and Carbon).
  • Are poor conductors of heat and electricity (Graphite, an allotrope of carbon, is an exception).
  • Solid non-metals are typically brittle.
  • Are neither malleable nor ductile.
  • Non-metallic character generally increases across a period from left to right and decreases down a group.
• Metalloids (Semi-metals):
  • Elements located along the thick zig-zag line separating metals from non-metals in the p-block (e.g., Silicon (Si), Germanium (Ge), Arsenic (As), Antimony (Sb), Tellurium (Te)). Boron (B) and Polonium (Po) are sometimes also considered metalloids.
  • They exhibit properties that are intermediate between those of metals and non-metals. For instance, they are often semiconductors.

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Problem 3.4. Considering the atomic number and position in the periodic table, arrange the following elements in the increasing order of metallic character : Si, Be, Mg, Na, P.

Answer:

The metallic character of elements increases down a group and decreases across a period from left to right.

Let's identify the positions of the given elements in the Periodic Table:

• Na ($Z=11$): Group 1, Period 3 (Alkali metal, highly metallic)
• Mg ($Z=12$): Group 2, Period 3 (Alkaline earth metal, metallic)
• Al ($Z=13$): Group 13, Period 3 (Metal)
• Si ($Z=14$): Group 14, Period 3 (Metalloid)
• P ($Z=15$): Group 15, Period 3 (Non-metal)
• Be ($Z=4$): Group 2, Period 2 (Alkaline earth metal, metallic)

Across Period 3 (Na, Mg, Si, P), metallic character decreases from left to right: Na > Mg > Si > P.

Down Group 2 (Be, Mg), metallic character increases: Be < Mg.

Now, let's compare all the given elements (Si, Be, Mg, Na, P).

Na (Group 1) is more metallic than Mg (Group 2) in the same period. Both are more metallic than Si (Group 14) and P (Group 15) in the same period.

Comparing Mg and Be (same group), Mg is below Be, so Mg is more metallic than Be.

Comparing Si and P (same period), Si is to the left of P, so Si is more metallic than P.

Ranking based on position:

• Na is most metallic among these.
• Mg is less metallic than Na, but more metallic than Si and P.
• Be is less metallic than Mg, but more metallic than Si and P (as metals are generally more metallic than metalloids/non-metals).
• Si is a metalloid, more metallic than the non-metal P.
• P is the least metallic (most non-metallic) among these.

Rough order of metallic character:

P (least metallic) < Si < Be < Mg < Na (most metallic).

The increasing order of metallic character is: P < Si < Be < Mg < Na.

Periodic Trends In Properties Of Elements

Many physical and chemical properties of elements show observable patterns or trends as we move across a period or down a group in the Periodic Table. These periodic trends are fundamentally linked to the electronic structure of atoms.

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Trends In Physical Properties

We will discuss the periodic trends for several key physical properties:

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(a) Atomic Radius

Defining and measuring the size of an atom is challenging because atoms are extremely small ($\approx 10^{-10}$ m) and the electron cloud surrounding the nucleus doesn't have a sharp boundary. Atomic radius is typically estimated based on the distance between the nuclei of bonded atoms:

• Covalent Radius: Half the distance between the nuclei of two identical atoms joined by a single covalent bond in a molecule (used for non-metals). Example: In Cl$_2$, the bond distance is 198 pm, so the covalent radius of Cl is 99 pm.
• Metallic Radius: Half the distance between the nuclei of adjacent atoms in a metallic crystal (used for metals). Example: In solid copper, the distance between adjacent atoms is 256 pm, so the metallic radius of Cu is 128 pm.
• Van der Waals Radius: Half the internuclear distance between two identical non-bonded atoms in adjacent molecules in the solid state (used for noble gases or between non-bonded atoms in molecular solids). These values are generally larger than covalent or metallic radii.

In simplified terms, "Atomic Radius" often refers to either covalent or metallic radius, depending on the element's type. Atomic radii are determined using techniques like X-ray diffraction.

Periodic Trends in Atomic Radius:

• Across a Period (Left to Right): Atomic radius generally decreases.
  This is because, across a period, electrons are added to the same valence shell ($n$ is constant). The nuclear charge ($Z$) increases with atomic number, leading to a greater attractive force between the nucleus and the valence electrons. Although there is some shielding from inner electrons, the increased nuclear attraction is more significant, pulling the valence shell closer to the nucleus and reducing the atomic size.
• Down a Group (Top to Bottom): Atomic radius generally increases.
  As you move down a group, new electron shells corresponding to higher principal quantum numbers ($n$) are added. The valence electrons are further from the nucleus, increasing the atomic size. The inner electrons effectively "shield" the valence electrons from the full positive charge of the nucleus, reducing the effective nuclear attraction they experience. This increased shielding and the larger $n$ value outweigh the effect of the increasing nuclear charge, leading to a larger atomic radius down a group.

Atom (Period II)	Li	Be	B	C	N	O	F
Atomic radius (pm)	152	111	88	77	74	66	64
Atom (Period III)	Na	Mg	Al	Si	P	S	Cl
Atomic radius (pm)	186	160	143	117	110	104	99

Atom (Group I)	Atomic Radius (pm)	Atom (Group 17)	Atomic Radius (pm)
Li	152	F	64
Na	186	Cl	99
K	231	Br	114
Rb	244	I	133
Cs	262	At	140

Noble gases' atomic radii are often listed as Van der Waals radii, which are significantly larger than covalent or metallic radii of other elements in the same period. Comparing them directly requires using consistent types of radii.

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(b) Ionic Radius

When an atom loses electrons, it forms a positively charged ion called a cation. When it gains electrons, it forms a negatively charged ion called an anion. Ionic radii are estimated from the distances between ions in ionic crystals.

• Cation vs. Parent Atom: A cation is always smaller than its neutral parent atom. This is because the cation has fewer electrons but the same nuclear charge, leading to a stronger attraction of the remaining electrons to the nucleus and a contraction of the electron cloud. For instance, the radius of $\text{Na}^+$ (95 pm) is much smaller than the atomic radius of Na (186 pm).
• Anion vs. Parent Atom: An anion is always larger than its neutral parent atom. Adding one or more electrons increases electron-electron repulsion within the same valence shell (or adds to a higher shell), effectively increasing the size of the electron cloud and decreasing the effective nuclear charge per electron. For instance, the radius of $\text{F}^-$ (136 pm) is larger than the atomic radius of F (64 pm).

Isoelectronic Species: These are atoms or ions that have the same total number of electrons. Examples include $\text{O}^{2-}$, $\text{F}^-$, Ne, $\text{Na}^+$, $\text{Mg}^{2+}$, and $\text{Al}^{3+}$, all having 10 electrons. In a series of isoelectronic species, the size is determined by the nuclear charge ($Z$).

• Among isoelectronic cations, the one with the higher positive charge (and thus higher nuclear charge) has a smaller radius due to stronger electron-nucleus attraction (e.g., $\text{Mg}^{2+}$ is smaller than $\text{Na}^+$).
• Among isoelectronic anions, the one with the higher negative charge (more electrons, lower $Z_{eff}$) has a larger radius due to increased electron-electron repulsion (e.g., $\text{O}^{2-}$ is larger than $\text{F}^-$).

Thus, for the isoelectronic series $\text{O}^{2-}, \text{F}^-, \text{Ne}, \text{Na}^+, \text{Mg}^{2+}, \text{Al}^{3+}$ (all 10 electrons), the size decreases as the nuclear charge increases: $\text{O}^{2-} > \text{F}^- > \text{Ne} > \text{Na}^+ > \text{Mg}^{2+} > \text{Al}^{3+}$.

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(c) Ionization Enthalpy ($\Delta_i H$)

Ionization enthalpy is the energy required to remove the most loosely bound electron from an isolated gaseous atom in its ground state. It quantifies how easily an atom loses an electron to form a positive ion (cation).

First Ionization Enthalpy ($\Delta_i H_1$): $\text{X(g)} \rightarrow \text{X}^+\text{(g)} + \text{e}^-$

Second Ionization Enthalpy ($\Delta_i H_2$): $\text{X}^+\text{(g)} \rightarrow \text{X}^{2+}\text{(g)} + \text{e}^-$

And so on for successive electrons. Ionization enthalpies are always positive values, indicating energy must be absorbed (endothermic process). Successive ionization enthalpies increase ($\Delta_i H_1 < \Delta_i H_2 < \Delta_i H_3 < \dots$) because it becomes harder to remove an electron from an increasingly positive ion.

Periodic Trends in Ionization Enthalpy:

• Across a Period (Left to Right): Ionization enthalpy generally increases.
  This is due to the decrease in atomic size and the increase in effective nuclear charge across a period. Valence electrons are held more tightly by the nucleus, requiring more energy to remove them.
• Down a Group (Top to Bottom): Ionization enthalpy generally decreases.
  As atomic size increases down a group, the outermost electron is further from the nucleus and experiences increased shielding from inner electrons. The reduced effective nuclear attraction makes it easier to remove the electron, thus lowering the ionization enthalpy.

Deviations from the general trend across a period:

• Group 2 vs Group 13: The first ionization enthalpy of Group 13 elements (like B) is slightly lower than that of Group 2 elements (like Be) in the same period. For Be ($1s^22s^2$), the electron is removed from the stable, filled 2s orbital. For B ($1s^22s^22p^1$), the electron is removed from the 2p orbital, which is higher in energy than 2s. The 2p electron is also slightly more shielded from the nucleus by the 2s electrons than the 2s electrons shield each other. This makes it easier to remove the 2p electron from B than a 2s electron from Be.
• Group 15 vs Group 16: The first ionization enthalpy of Group 16 elements (like O) is slightly lower than that of Group 15 elements (like N) in the same period. N ($1s^22s^22p^3$) has a half-filled and stable 2p subshell (according to Hund's rule, each 2p orbital has one electron with parallel spins). O ($1s^22s^22p^4$) has one 2p orbital with two paired electrons, leading to increased electron-electron repulsion compared to the half-filled configuration. This repulsion makes it easier to remove one electron from O than from N.

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(d) Electron Gain Enthalpy ($\Delta_{eg} H$)

Electron gain enthalpy is the enthalpy change that occurs when an electron is added to an isolated gaseous atom in its ground state to form a negative ion (anion).

$\text{X(g)} + \text{e}^- \rightarrow \text{X}^-\text{(g)}$

This process can be exothermic ($\Delta_{eg} H$ is negative, energy is released) or endothermic ($\Delta_{eg} H$ is positive, energy is absorbed).

• If energy is released upon electron gain (exothermic), the process is favourable, and the element has a high electron affinity (tendency to gain electrons). Halogens (Group 17) have very negative $\Delta_{eg} H$ values as gaining an electron completes their valence shell to a stable noble gas configuration.
• If energy is required to force the atom to accept an electron (endothermic), $\Delta_{eg} H$ is positive. Noble gases (Group 18) have positive $\Delta_{eg} H$ values because the added electron must enter a higher, empty energy level, resulting in an unstable configuration and significant electron-electron repulsion.

Periodic Trends in Electron Gain Enthalpy:

• Across a Period (Left to Right): Electron gain enthalpy generally becomes more negative.

  Group 1	$\Delta_{eg}H$	Group 16	$\Delta_{eg}H$	Group 17	$\Delta_{eg}H$	Group 0	$\Delta_{eg}H$
  H	– 73	O	– 141	F	– 328	He	+ 48
  Li	– 60	S	– 200	Cl	– 349	Ne	+ 116
  Na	– 53	Se	– 195	Br	– 325	Ar	+ 96
  K	– 48	Te	– 190	I	– 295	Kr	+ 96

  This trend is due to the increasing effective nuclear charge and decreasing atomic size across a period. A smaller atom with a higher positive nuclear charge attracts the incoming electron more strongly, leading to a greater release of energy.
• Down a Group (Top to Bottom): Electron gain enthalpy generally becomes less negative. As atomic size increases down a group, the added electron is further from the nucleus and experiences weaker attraction. This results in less energy released or even energy required to add an electron.

Exceptions to the trend down a group (especially in Period 2): The electron gain enthalpies of elements in the second period (like O and F) are often less negative than those of the corresponding elements in the third period (S and Cl). This is because the second-period elements are unusually small. When an electron is added to the relatively small 2p subshell of O or F, it experiences significant repulsion from the electrons already present in the small volume. In contrast, for S or Cl, the added electron enters the larger 3p subshell, where electron-electron repulsion is less significant, leading to a more negative electron gain enthalpy.

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(e) Electronegativity

Electronegativity is a qualitative measure of the ability of an atom to attract shared electrons towards itself when it is in a chemical compound (i.e., when it is bonded to another atom). Unlike ionization enthalpy or electron gain enthalpy, it is not a property of an isolated atom and cannot be directly measured experimentally. Several scales exist to assign numerical values (e.g., Pauling scale, Mulliken-Jaffe scale, Allred-Rochow scale). The most common is the Pauling scale, where Fluorine is assigned the highest value of 4.0.

Periodic Trends in Electronegativity:

• Across a Period (Left to Right): Electronegativity generally increases.

  Atom (Period II)	Li	Be	B	C	N	O	F
  Electronegativity	1.0	1.5	2.0	2.5	3.0	3.5	4.0
  Atom (Period III)	Na	Mg	Al	Si	P	S	Cl
  Electronegativity	0.9	1.2	1.5	1.8	2.1	2.5	3.0

  As atomic size decreases and effective nuclear charge increases across a period, the nucleus's attraction for shared electrons in a bond becomes stronger.
• Down a Group (Top to Bottom): Electronegativity generally decreases.

  Atom (Group I)	Electronegativity Value	Atom (Group 17)	Electronegativity Value
  Li	1.0	F	4.0
  Na	0.9	Cl	3.0
  K	0.8	Br	2.8
  Rb	0.8	I	2.5
  Cs	0.7	At	2.2

  As atomic size increases down a group, the valence electrons (including shared ones in a bond) are further from the nucleus and experience greater shielding, reducing the nucleus's ability to attract them.

Electronegativity is closely related to non-metallic character (ability to gain electrons) and inversely related to metallic character (tendency to lose electrons). High electronegativity corresponds to high non-metallic character. Low electronegativity corresponds to high metallic character.

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Periodic Trends In Chemical Properties

Periodic trends are also evident in the chemical properties of elements, such as valence, oxidation states, and reactivity.

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(a) Periodicity of Valence or Oxidation States

The valence of an element, representing its combining capacity, is primarily determined by the number of electrons in its outermost shell. For representative (s-block and p-block) elements, the valence is often equal to the number of valence electrons (Group 1 and 2) or eight minus the number of valence electrons (Group 15-17). Group 18 elements (noble gases) have a valence of 0 (or sometimes 8).

The oxidation state of an element in a compound refers to the apparent charge on an atom based on the assumption that all bonds are ionic, with the more electronegative atom assigned the negative charge. Oxidation states can be positive or negative and often variable, especially for d and f block elements.

Periodic trends in valence (shown by common hydrides and oxides) (Table 3.9):

Group	1	2	13	14	15	16	17
Number of valence electrons	1	2	3	4	5	6	7
Valence (common)	1	2	3	4	3, 5	2, 6	1, 7
Formula of hydride (Examples)	LiH, NaH, KH	MgH$_2$, CaH$_2$	B$_2$H$_6$, AlH$_3$	CH$_4$, SiH$_4$, GeH$_4$, SnH$_4$	NH$_3$, PH$_3$, AsH$_3$, SbH$_3$	H$_2$O, H$_2$S, H$_2$Se, H$_2$Te	HF, HCl, HBr, HI
Formula of oxide (Examples)	Li$_2$O, Na$_2$O, K$_2$O	MgO, CaO, SrO, BaO	B$_2$O$_3$, Al$_2$O$_3$, Ga$_2$O$_3$, In$_2$O$_3$	CO$_2$, SiO$_2$, GeO$_2$, SnO$_2$, PbO$_2$	N$_2$O$_3$, N$_2$O$_5$, P$_4$O$_6$, P$_4$O$_{10}$, As$_2$O$_3$, As$_2$O$_5$, Sb$_2$O$_3$, Sb$_2$O$_5$, Bi$_2$O$_3$	SO$_3$, SeO$_3$, TeO$_3$	Cl$_2$O$_7$

Many elements, particularly transition and inner-transition metals, exhibit multiple oxidation states due to the involvement of inner d or f electrons in bonding.

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(b) Anomalous Properties of Second Period Elements

The first element in each group of the s-block (Li, Be) and p-block (B, C, N, O, F) exhibits properties that are significantly different from the rest of the elements in their respective groups. This is known as anomalous behaviour.

Reasons for anomalous behaviour of Period 2 elements (Li to F):

1. Small Size: They are the smallest elements in their groups.
2. High Electronegativity: They have the highest electronegativity values in their groups.
3. High Charge/Radius Ratio: For cations, this ratio is very high.
4. Absence of d-orbitals in the valence shell: Elements of the second period have only 2s and 2p orbitals (a total of four orbitals) in their valence shell ($n=2$), limiting their maximum covalency to 4. Elements from the third period onwards have empty d orbitals (e.g., 3s, 3p, 3d), allowing them to expand their valence shell and exhibit covalencies greater than 4 (e.g., Al can form $\text{AlF}_6^{3-}$).
5. Ability to form $p\pi - p\pi$ multiple bonds: Second-period elements (especially C, N, O, F) can form stable multiple bonds (double or triple bonds) by sideways overlap of their p orbitals with themselves (e.g., C=C, N$\equiv$N) and with other second-period elements (e.g., C=O, C$\equiv$N). Heavier elements in the same group have larger and more diffuse p orbitals, making $p\pi - p\pi$ overlap less effective, thus reducing their tendency to form strong multiple bonds.

Diagonal Relationship: The anomalous behaviour of second-period elements often leads to a similarity in properties between the first element of a group and the second element of the *next* group. This is called the diagonal relationship. Examples: Lithium (Group 1) shows similarities with Magnesium (Group 2), and Beryllium (Group 2) shows similarities with Aluminium (Group 13).

Property	Element
Metallic radius (pm)	Li (152)	Be (111)	B (88)
	Na (186)	Mg (160)	Al (143)
Ionic radius M$^+$ / M$^{2+}$ / M$^{3+}$ (pm)	Li$^+$ (76)	Be$^{2+}$ (31)
	Na$^+$ (102)	Mg$^{2+}$ (72)	Al$^{3+}$ (53.5)

Li ($Z/r \approx 76/76 = 1.0$) and Mg ($Z/r^2 \approx 12/72^2$? This is charge/radius, not charge/radius squared. Let's use ionic charge and ionic radius $Li^+ (1+, 76pm), Mg^{2+} (2+, 72pm), Al^{3+} (3+, 53.5pm)$ approx charge density $1/76, 2/72, 3/53.5$. The ratio is not simple) exhibit similar charge density ($Z/\text{radius}$ or $Z/\text{radius}^2$ for ions) which leads to comparable polarizing power and similarities in properties, such as forming covalent compounds more readily than other alkali/alkaline earth metals.

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Periodic Trends And Chemical Reactivity

The chemical reactivity of elements is closely related to their tendency to lose or gain electrons, which is reflected in properties like ionization enthalpy and electron gain enthalpy.

• Across a Period (Left to Right): Chemical reactivity is highest at the two extremes (Group 1 and Group 17) and lowest towards the centre (Groups 14-15).
  • On the extreme left (Alkali metals, Group 1), elements have low ionization enthalpies and readily lose electrons to form cations. Their reactivity is high due to their strong tendency to lose electrons.
  • On the extreme right (Halogens, Group 17), elements have high negative electron gain enthalpies and readily gain electrons to form anions. Their reactivity is high due to their strong tendency to gain electrons. (Noble gases, Group 18, are exceptions as they are generally unreactive due to stable electron configurations).
  • Elements in the centre (like Group 14) have intermediate ionization enthalpies and electron gain enthalpies, showing less tendency to lose or gain electrons fully, and often form covalent bonds. They are generally less reactive than elements at the extremes.
• Down a Group (Top to Bottom):
  • For metals (like Alkali metals, Group 1), reactivity generally increases down the group. This is because ionization enthalpy decreases as size increases and effective nuclear attraction for valence electrons weakens, making it easier to lose electrons.
  • For non-metals (like Halogens, Group 17), reactivity generally decreases down the group. Although electron gain enthalpy becomes less negative, the dominant factor is the decreasing attraction for an incoming electron due to increasing size and shielding. Thus, their ability to gain electrons decreases down the group.

The chemical nature of oxides provides insight into reactivity. Oxides of metals are generally basic, reacting with water to form bases. Oxides of non-metals are generally acidic, reacting with water to form acids. Oxides of elements in the middle of the table can be amphoteric (reacting with both acids and bases) or neutral.

• Oxides of elements on the extreme left of a period (e.g., $\text{Na}_2\text{O}$) are typically most basic.
• Oxides of elements on the extreme right of a period (e.g., $\text{Cl}_2\text{O}_7$) are typically most acidic.
• Oxides in the centre can be amphoteric (e.g., $\text{Al}_2\text{O}_3$) or neutral (e.g., CO, NO).

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