JEE Mains Chemistry · Formula sheet

Classification of Elements and Periodicity formulas

4 formulas, 13 reference tables and 25 common traps for JEE Mains Chemistry Classification of Elements and Periodicity, grouped by subtopic.

Full notes with worked examples

Periodic Law, Blocks and Position in the Table

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Names for Z above 100 and the block from Z

Temporary IUPAC name

\text{name} = \text{root}(d_1) + \text{root}(d_2) + \text{root}(d_3) + \text{ium}

Placing an element from its configuration or an ion

Recover Z from an ion

Z = e^{-} + q \qquad A = Z + n

$q$ charge on the ion, with its sign (−3 for an ion X³⁻)
$n$ number of neutrons

From atomic weight to atomic number

Who and when	Sorted by	What they found
Döbereiner, 1829	Atomic weight	Triads such as Li, Na, K: the middle atomic weight is about the mean of the other two
Newlands, 1865	Atomic weight	Law of octaves: every eighth element repeats the first; it worked only up to calcium
Lothar Meyer, 1869	Atomic weight	Plotted atomic volume against atomic weight and saw a repeating curve
Mendeleev, 1869	Atomic weight	Left gaps and predicted eka-aluminium (Ga) and eka-silicon (Ge); reversed some pairs to keep families together
Moseley, 1913	Atomic number	A plot of $\sqrt{\nu}$ against $Z$ is a straight line, so $Z$ is the true basis Only Moseley's work uses atomic number. A statement giving Newlands or Meyer atomic numbers is false.
Modern table	Atomic number	18 groups and 7 periods; blocks s, p, d and f named by the subshell being filled

Everyone before 1913 used atomic weight; the modern law and table use atomic number.

Common traps

Twice the orbitals, not equal to them

Period 2 fills four orbitals (2s and three 2p) and holds eight elements. A statement that the number of elements equals the number of orbitals is false; each orbital takes two electrons.

Group, not period

Elements with similar outer configurations are stacked in one group. Along a period the outer configuration changes at every step, so a statement placing them in the same period is false.

Count the electrons before naming

When the question gives a configuration, add the core and every electron first.

[\mathrm{Rn}]

is 86, so a configuration ending

5f^{14}6d^{2}7s^{2}

Z = 104

, not a number read off the last subshell.

Adding the charge the wrong way

An anion has MORE electrons than protons. For

\mathrm{X^{2-}}

with 10 electrons,

Z = 8

, not 12. Write

Z = e^{-} + q

with the sign of the charge and the direction takes care of itself.

Atomic and Ionic Radii

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Counting electrons to find isoelectronic species

Counting particles

e^{-} = Z - q \qquad n = A - Z

$q$ charge on the species, with its sign
$A$ mass number

Atomic radius across a period and down a group

Series	Atomic radius (pm)	Trend
Period 2	Li 152, Be 111, B 88, C 77, N 74, O 66, F 64	Falls steadily across
Period 3	Na 186, Mg 160, Al 143, Si 117, P 110, S 104, Cl 99	Falls steadily across
Group 1	Li 152, Na 186, K 231, Rb 244, Cs 262	Rises down the group
Group 17	F 64, Cl 99, Br 114, I 133, At 140	Rises down the group
Period 4 ends	K 231, Br 114	Largest and smallest in period 4, noble gas excluded

Compare the columns: Be (111) is smaller than Mg (160) and Mg is larger than Al (143).

Ionic radius and isoelectronic series

Species	Protons	Electrons	Radius (pm)
Na atom	11	11	186
$\mathrm{Na^+}$	11	10	102
Cl atom	17	17	99
$\mathrm{Cl^-}$	17	18	184
$\mathrm{O^{2-}}$	8	10	140 Isoelectronic with $\mathrm{Mg^{2+}}$ (72 pm), yet about twice as large: the same electrons do not mean the same size.
$\mathrm{F^-}$	9	10	133
$\mathrm{Mg^{2+}}$	12	10	72
$\mathrm{Al^{3+}}$	13	10	53.5
$\mathrm{K^+}$	19	18	138

Within the 10-electron rows, every extra proton makes the ion smaller.

Common traps

Half the bond, not double

The covalent radius is half the distance between the two nuclei in

\mathrm{Cl_2}

. A statement that it is double the atomic radius has the relation upside down.

Down a group beats across a period

Be is at the left of period 2 but still smaller than Mg, which has one more shell. When an order mixes groups and periods, compare the shells first.

Isoelectronic does not mean the same size

\mathrm{O^{2-}}

and

\mathrm{Mg^{2+}}

both have 10 electrons, but Mg has 12 protons against oxygen's 8. The claim that their radii are equal is false even though the reason (both are isoelectronic) is true.

Isoelectronic ions have different nuclear charges

The whole point of the series is that Z changes while the electron count does not. A statement that

\mathrm{O^{2-}}

\mathrm{F^-}

\mathrm{Na^+}

and

\mathrm{Mg^{2+}}

have the same nuclear charge is false.

A neutral atom is not its ion

Na has 11 electrons and

\mathrm{Na^+}

has 10. In a list that mixes atoms and ions, count each one separately: Al and Mg are not in the 10-electron set, while

\mathrm{Al^{3+}}

and

\mathrm{Mg^{2+}}

are.

Ionization Enthalpy

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Successive ionization enthalpies and the energy for a mass

Energy to ionize a mass of gaseous atoms

E = \frac{m}{M}\,\left(\Delta_i H_1 + \Delta_i H_2 + \dots\right)

$m$ mass of the gaseous atoms, in g
$M$ molar mass, in g mol⁻¹

First ionization enthalpy across a period

Group	Period 2 (kJ mol⁻¹)	Period 3 (kJ mol⁻¹)	Why
1	Li 520	Na 496	One s electron outside a noble-gas core: lowest in the period
2	Be 899	Mg 737	Filled $ns^2$ subshell
13	B 801	Al 577	Dip: the lone $np$ electron is less penetrating Group 13 sits BELOW group 2. The option with a smooth rise (Be < B) is the trap.
14	C 1086	Si 786	Rises again
15	N 1402	P 1012	Half-filled $np^3$ : extra stable
16	O 1314	S 1000	Dip: pairing in $np^4$ adds repulsion Group 16 sits BELOW group 15: N > O and P > S.
17	F 1681	Cl 1256	Rises again
18	Ne 2080	Ar 1520	Filled shell: highest in the period

Read down each column for the period order; the two amber rows are the exceptions every question tests.

Down a group, and where it fails

Group	First ionization enthalpy (kJ mol⁻¹)	Order and exception
1	Li 520, Na 496, K 419, Rb 403, Cs 376	Steady fall
2	Be 899, Mg 737, Ca 590, Sr 549, Ba 503	Steady fall
13	B 801, Al 577, Ga 579, In 558, Tl 589	B > Tl > Ga > Al > In Ga is not below Al, and Tl is above both.
13, second	B 2427, Al 1816, Ga 1979, In 1820, Tl 1971	B > Ga > Tl > In > Al
14	C 1086, Si 786, Ge 761, Sn 708, Pb 715	C > Si > Ge > Pb > Sn Pb is above Sn.
18	He 2372, Ne 2080, Ar 1520, Kr 1351, Xe 1170, Rn 1037	Steady fall; Rn lowest

The exceptions appear only after a filled d or f subshell: from Ga, Tl and Pb onwards.

Common traps

The smooth order is the wrong option

Li < Be < B < C < N < O < F looks right and is always offered. It misses both dips. The true order swaps two pairs: Li < B < Be < C < O < N < F.

A simple fall down group 13 or 14 is wrong

An order like Al > Ga or Sn > Pb applies the group rule blindly. Poor shielding by d and f electrons lifts Ga and Pb. Check these two pairs before choosing.

Negative or smaller second values

Options such as −856 kJ mol⁻¹ or 590 kJ mol⁻¹ for the second ionization enthalpy of Mg are impossible. The second value must be positive and larger than 737.

Second ionization compares the cations

For IE₂, look at the ion that loses the electron.

\mathrm{O^+}

2p^3

and

\mathrm{N^+}

2p^2

, so the dip moves one place: O is above F for IE₂, the reverse of the first ionization order.

Electron Gain Enthalpy

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When electron gain releases energy and when it costs energy

Atom	Electron gain enthalpy (kJ mol⁻¹)	Sign	Why
He	+48	Endothermic	Electron must enter the $2s$ shell
Ne	+116	Endothermic	Most positive noble gas; the electron enters $3s$
Ar	+96	Endothermic	Same value as Kr
Kr	+96	Endothermic	Same value as Ar
Xe	+77	Endothermic	Larger atom, smaller cost
Li	−60	Exothermic	Half-filled $2s$ takes a second s electron
Na	−53	Exothermic	Small but negative
Cl	−349	Exothermic	Most negative of all elements

The largest gap between two elements is Ne and Cl:

116 - (-349) = 465

kJ mol⁻¹.

Groups 16 and 17: why Cl beats F and S beats O

Group	Electron gain enthalpy (kJ mol⁻¹)	Order by magnitude
17	F −328, Cl −349, Br −325, I −295, At −270	Cl > F > Br > I > At F is second, not first. Cl is the most negative element in the table.
16	O −141, S −200, Se −195, Te −190, Po −174	S > Se > Te > Po > O O is the least negative in group 16, below even Po.
1	Li −60, Na −53, K −48, Rb −47, Cs −46	Li > Na > K > Rb ≈ Cs
Hydrogen	H −73	More negative than any alkali metal

Down each group the value becomes less negative, except that the first member of groups 16 and 17 is out of place.

Common traps

Neon, not helium, is the most positive

Helium's value (+48) is the smallest of the noble gases, and neon's (+116) the largest. Ar and Kr are equal at +96, which is why options that separate them need care.

Electron affinity flips the sign

A question that says the electron affinity is negative for Be, N and O → O²⁻ means those processes absorb energy. Electron affinity counts energy released, so it has the opposite sign to

\Delta_{eg}H

F is not the most negative

Fluorine has the highest electronegativity, but not the most negative electron gain enthalpy. Its small

2p

shell repels the added electron. Any statement that F's value is more negative than Cl's is false.

Signed or magnitude

"S > Se > Te > O" is right by magnitude and wrong on signed values. When one option is the exact reverse of another, the paper is testing which reading it means; pick the one consistent with the other statements in the question.

Electronegativity and Metallic Character

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Electronegativity on the Pauling scale

Series	Pauling electronegativity	Trend
Period 2	Li 1.0, Be 1.5, B 2.0, C 2.5, N 3.0, O 3.5, F 4.0	Rises across
Period 3	Na 0.9, Mg 1.2, Al 1.5, Si 1.8, P 2.1, S 2.5, Cl 3.0	Rises across
Group 1	Li 1.0, Na 0.9, K 0.8, Rb 0.8, Cs 0.7	Falls down
Group 17	F 4.0, Cl 3.0, Br 2.8, I 2.5, At 2.2	Falls down
Group 13	B 2.0, Al 1.5, Ga 1.6, In 1.7, Tl 1.8	Falls from B to Al, then rises slightly Poor shielding by d and f electrons again: Ga, In and Tl are above Al.

Values from the Pauling scale; the trend, not the second decimal, is what the questions test.

Metallic character and reactivity

Compare	More metallic	Reason
Na and Mg	Na	Left of Mg in period 3
Mg and Al	Mg	Left of Al in period 3
Be and Mg	Mg	Below Be in group 2
K and Ca	K	Left of Ca in period 4
Be and Si	Be	Si is a metalloid; Be is a metal
N, P, O, S, Cl, F	P most, F least	P is lowest and furthest left; F is top right

Down and to the left means more metallic.

Metals, non-metals, metalloids and diagonal pairs

Element	Z	Group	Class
B	5	13	Metalloid
Si	14	14	Metalloid
Ge	32	14	Metalloid
As	33	15	Metalloid
Sb	51	15	Metalloid
Te	52	16	Metalloid
I	53	17	Non-metal
Bi	83	15	Metal
Pb	82	14	Metal

The metalloids run diagonally from B down to Te; Bi and Pb below them are metals.

Common traps

Electronegativity is not a constant

Unlike ionization enthalpy, electronegativity belongs to an atom in a bond. The same element has different values in different compounds, so a statement that it depends on the bonded atom is correct.

Atomic radius is not always larger than ionic radius

A statement pairing a correct metallic order with "atomic radius is always greater than ionic radius" is half false: an anion is larger than its atom. Judge each statement on its own.

Bismuth is a metal

As and Sb in group 15 are metalloids, but Bi below them is a metal. Group 15 runs the whole range: N and P are non-metals, As and Sb metalloids, Bi a metal.

Nature of Oxides and Group 14 Trends

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Oxides across a period: basic to acidic

Oxide	Nature	With water
$\mathrm{Na_2O}$	Strongly basic	$\mathrm{Na_2O + H_2O \to 2NaOH}$
$\mathrm{MgO}$	Basic	Forms $\mathrm{Mg(OH)_2}$ , sparingly soluble
$\mathrm{Al_2O_3}$	Amphoteric	Insoluble; dissolves in both acids and alkalis
$\mathrm{SiO_2}$	Acidic	Insoluble; reacts with hot NaOH to give a silicate
$\mathrm{P_4O_{10}}$	Acidic	$\mathrm{P_4O_{10} + 6H_2O \to 4H_3PO_4}$
$\mathrm{SO_3}$	Acidic	$\mathrm{SO_3 + H_2O \to H_2SO_4}$
$\mathrm{Cl_2O_7}$	Strongly acidic	$\mathrm{Cl_2O_7 + H_2O \to 2HClO_4}$

Period 3 oxides in their highest oxidation states, from sodium to chlorine.

Acidic, basic, amphoteric and neutral oxides

Element	Low oxidation state oxide	High oxidation state oxide
Nitrogen	$\mathrm{N_2O}$ , NO: neutral	$\mathrm{N_2O_3}$ , $\mathrm{NO_2}$ , $\mathrm{N_2O_5}$ : acidic
Carbon	CO: neutral	$\mathrm{CO_2}$ : acidic
Vanadium	$\mathrm{V_2O_3}$ : basic	$\mathrm{V_2O_5}$ : amphoteric
Chromium	CrO: basic; $\mathrm{Cr_2O_3}$ : amphoteric	$\mathrm{CrO_3}$ : acidic
Manganese	MnO: basic	$\mathrm{Mn_2O_7}$ : acidic
Sulphur	$\mathrm{SO_2}$ : acidic	$\mathrm{SO_3}$ : more strongly acidic

For one element, the higher the oxidation state, the more acidic the oxide.

Group 14: oxides, inert pair effect and bond strength

Element	Class	Oxides	Electronegativity	Melting point (K)
C	Non-metal	CO neutral, $\mathrm{CO_2}$ acidic	2.5	4373
Si	Metalloid	$\mathrm{SiO_2}$ acidic	1.8	1693
Ge	Metalloid	GeO and $\mathrm{GeO_2}$ acidic	1.8	1218
Sn	Metal	SnO and $\mathrm{SnO_2}$ amphoteric	1.8	505 Tin has the lowest melting point in the group, below lead.
Pb	Metal	PbO and $\mathrm{PbO_2}$ amphoteric	1.9	600

Electronegativity does not fall steadily from Si to Pb: it stays at 1.8 and then rises to 1.9.

Common traps

CO is not acidic

\mathrm{CO_2}

is acidic, but CO is neutral: it forms no acid with water and does not react with alkalis. Do not carry the nature of one oxide of an element over to another.

Not every nitrogen oxide is acidic

\mathrm{N_2O}

and NO are neutral, while

\mathrm{N_2O_3}

\mathrm{NO_2}

and

\mathrm{N_2O_5}

are acidic. In a counting question, sort the nitrogen oxides one by one.

NO is neutral, not amphoteric

\mathrm{Al_2O_3}

is amphoteric, but NO reacts with neither acids nor bases. A statement that calls both amphoteric is false.

GeO is not amphoteric

SnO and PbO are amphoteric, and it is tempting to extend that to GeO. Germanium's monoxide is distinctly acidic, like its dioxide.

Lowest melting point is tin, not lead

Lead is lower in the group, but tin melts at 505 K and lead at 600 K. The melting points fall from C to Sn and rise again at Pb.

Classification of Elements and Periodicity formulas

Periodic Law, Blocks and Position in the Table

Names for Z above 100 and the block from Z

Placing an element from its configuration or an ion

From atomic weight to atomic number

Common traps

Atomic and Ionic Radii

Counting electrons to find isoelectronic species

Atomic radius across a period and down a group

Ionic radius and isoelectronic series

Common traps

Ionization Enthalpy

Successive ionization enthalpies and the energy for a mass

First ionization enthalpy across a period

Down a group, and where it fails

Common traps

Electron Gain Enthalpy

When electron gain releases energy and when it costs energy

Groups 16 and 17: why Cl beats F and S beats O

Common traps

Electronegativity and Metallic Character

Electronegativity on the Pauling scale

Metallic character and reactivity

Metals, non-metals, metalloids and diagonal pairs

Common traps

Nature of Oxides and Group 14 Trends

Oxides across a period: basic to acidic

Acidic, basic, amphoteric and neutral oxides

Group 14: oxides, inert pair effect and bond strength

Common traps

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