The d- and f-Block Elements Formula Sheet — JEE Main Chemistry

Every key The d- and f-Block Elements formula, definition and theorem for JEE Main Chemistry in one place — with common examiner traps and worked examples. Free to read; blurt from memory, then check your gaps.

Syllabus — topics coveredNTA · 18 sub-topics

Transition elements - general introduction
Electronic configuration
Occurrence and characteristics
General trends in first-row transition elements
Physical properties
Ionization enthalpy
Oxidation states
Atomic radii
Colour
Catalytic behaviour
Magnetic properties
Complex formation
Interstitial compounds
Alloy formation
Preparation, properties and uses of K₂Cr₂O₇ and KMnO₄
Inner transition elements
Lanthanoids: electronic configuration, oxidation states, lanthanoid contraction
Actinoids: electronic configuration and oxidation states

Position & Electronic Configuration

Transition element (IUPAC): An element whose atom

or

a stable ion has a

partially filled

d subshell. They occupy

Groups 3-12

between the s- and p-blocks, in three complete series:

3 d

(Sc→Zn),

4 d

(Y→Cd) and

5 d

(La, Hf→Hg); the

6 d

series is incomplete.

Series	Elements	Subshell filled
$3 d$	Sc–Zn	$3 d$
$4 d$	Y–Cd	$4 d$
$5 d$	La, Hf–Hg	$5 d$
$6 d$	Ac, Rf… (incomplete)	$6 d$

General valence configuration

(n - 1) d^{1 - 10} n s^{1 - 2}

Inner

(n - 1) d

fills after the

n s

orbital; both take part in bonding.

🎯 Exam · Two configuration exceptions

Cr = [Ar] 3 d^{5} 4 s^{1}

and

Cu = [Ar] 3 d^{10} 4 s^{1}

— a half-filled (

d^{5}

) or fully-filled (

d^{10}

) set is extra-stable, so one

4 s

electron shifts into

3 d

⚠️ Watch out · Zn, Cd, Hg are NOT transition metals

Their configuration is

(n - 1) d^{10} n s^{2}

and they keep a

filled

d^{10}

shell in all their compounds (only

+ 2

state) — no partially filled d, so they fail the definition though they sit in the d-block.

Writing ion configurations

▸For cations remove $ns electrons first$ , then $(n - 1) d$ : $Fe = 3 d^{6} 4 s^{2} \Rightarrow F e^{2 +} = 3 d^{6}$ , $F e^{3 +} = 3 d^{5}$ .
▸ $S c^{3 +} (3 d^{0})$ and $Z n^{2 +} (3 d^{10})$ have no unpaired d electrons.
▸ $M n^{2 +} = 3 d^{5}$ — exactly half-filled, hence extra stable.

Why a 'transition' series?

▸They form a bridge — a $transition$ — between the highly electropositive s-block and the electronegative p-block.
▸ $(n - 1) d$ and $n s$ have similar energies, so the $d$ electrons are chemically active.
▸This shared involvement gives variable oxidation states, colour, magnetism, catalysis and complex formation (Pages 3–4).

🚫 Examiner Trap · Examiner traps

(1) A transition element has a partially filled d in the

atom OR a stable ion

— so Zn/Cd/Hg (

d^{10}

always) are NOT true transition metals. (2) Exceptions: Cr

= 3 d^{5} 4 s^{1}

, Cu

= 3 d^{10} 4 s^{1}

(half/full-filled stability). (3) For cations remove

ns first

, then

(n - 1) d

(Fe

^{3 +} = 3 d^{5}

). (4) Fill

4 s

before

3 d

, but ionise

4 s

before

3 d

Physical Properties & Atomic Trends

General physical character

▸Nearly all are hard, high-density metals with $high melting & boiling points$ , high tensile strength, malleable, ductile and good conductors of heat & electricity.
▸These follow from $strong metallic bonding$ involving the unpaired $(n - 1) d$ electrons in addition to ns.
▸Across a series the maxima occur near the middle, where the number of unpaired $d$ electrons (favouring interatomic bonding) is greatest.

Melting point of the 3d series rising to a maximum around vanadium and chromium then falling, with a sharp dip at manganese and the lowest value at zinc — Melting / atomisation enthalpy peak near $d^{5}$ ; Mn & Zn dip.

🎯 Exam · Why Mn and Zn dip

Mn (3 d^{5} 4 s^{2})

has a stable half-filled set whose electrons resist delocalisation, so its metallic bond (and m.p.) is weaker than its neighbours.

Zn (3 d^{10})

has

no unpaired

d electrons at all — only

n s^{2}

bonds, giving the lowest m.p.

Atomic & ionic radii along a series

▸Radius first $decreases$ (rising nuclear charge), then stays almost constant in the middle (d-electron screening offsets it), and rises slightly at the end.
▸Ionic radius falls as oxidation state rises: $M n^{2 +} > M n^{3 +} > M n^{4 +}$ .
▸Down a group $3 d \to 4 d$ radius increases, but $4 d \approx 5 d$ — see below.

★ Remember · Lanthanoid contraction → equal 4d/5d radii

The

4 f

electrons filled between La and Hf shield poorly, so the

5 d

elements are pulled in:

Zr (160 pm) \approx Hf (159 pm)

Nb \approx Ta

Mo \approx W

— making each

4 d

–

5 d

pair very hard to separate.

Ionisation enthalpy & density

▸ $I E_{1}$ rises only $irregularly and gently$ across a series (added d electron partly screens the nucleus) — unlike the steep p-block rise.
▸Densities are high and increase across (smaller atoms, heavier nuclei); $5 d$ metals are densest (Os, Ir).
▸Enthalpy of atomisation is high — strong metal–metal bonds (catalysis-relevant).

🚫 Examiner Trap · Examiner traps

(1) High m.p./hardness come from strong metallic bonding by

unpaired d

electrons — peaks near

d^{5}

. (2) Mn (

d^{5}

, stable half-filled) and Zn (

d^{10}

, no unpaired) DIP in m.p. (3) Lanthanoid contraction makes

Zr \approx Hf

(

4 d \approx 5 d

). (4) IE rises only gently/irregularly across a series (unlike the p-block).

Oxidation States & Standard Potentials

Variable oxidation states: Because

(n - 1) d

and ns electrons have similar energies, a transition metal can lose a

variable

number of electrons, giving several oxidation states that differ by

one

(e.g.

+ 2, + 3, + 4

) — unlike p-block states that differ by two.

Chart of oxidation states of the 3d series from scandium plus 3 only, rising to manganese showing plus 2 to plus 7, then falling to zinc plus 2, with the most stable state of each element highlighted — Maximum state peaks at Mn $(+ 7)$ ; $+ 2$ runs across the series.

Reading the trend

▸ $Sc$ shows only $+ 3$ ; the range widens to $Mn (+ 2 to + 7)$ , where $+ 7 =$ total valence electrons, then narrows again to $Zn (+ 2)$ .
▸The $+ 2$ state ( $n s^{2}$ loss) appears for almost every element and becomes more stable across the series.
▸Highest states ( $M n^{+ 7}$ , $C r^{+ 6}$ ) occur only with the most electronegative $O$ and $F$ (e.g. $Mn O_{4}^{-}$ , $Cr O_{4}^{2 -}$ , $V F_{5}$ ).

🎯 Exam · Stability rule of thumb

Half-filled or filled d sub-shells are favoured:

M n^{2 +} (d^{5})

and

F e^{3 +} (d^{5})

are especially stable, which is why

M n^{2 +}

is harder to oxidise than

F e^{2 +}

and

F e^{3 +}

is a common state.

Standard electrode potential

M^{2 +} (aq) + 2 e^{-} \to M (s)

E^{\circ}

is mostly negative ⇒ metals are electropositive and displace

H_{2}

from acids.

★ Remember · Copper is the exception

E_{C u^{2 +} /Cu}^{\circ} = + 0.34

V is

positive

— the high sublimation + ionisation enthalpy is not offset by hydration, so Cu does

not

liberate

H_{2}

from dilute acids (a 'noble' first-row metal).

Irregular E° values

▸ $E_{M^{2 +} /M}^{\circ}$ is irregular because it depends on $Δ_{s u b} H + Δ_{i o n} H + Δ_{h y d} H$ together, not one term.
▸ $E_{M n^{3 +} /M n^{2 +}}^{\circ} = + 1.5$ V (M $n^{3 +}$ strongly oxidising, reverts to stable $d^{5}$ ).
▸ $E_{C r^{3 +} /C r^{2 +}}^{\circ} = - 0.4$ V (C $r^{2 +}$ reducing, goes to stable $d^{3}$ C $r^{3 +}$ ).

🚫 Examiner Trap · Examiner traps

(1) Oxidation states differ by

one

(not two like p-block); max state peaks at Mn (

+ 7 =

group e

^{-}

). (2) Highest states need O/F (MnO

_{4}^{-}

, Cr

F_{6}

). (3)

E_{M^{2 +} / M}^{\circ}

is mostly negative (electropositive);

Cu is the exception

(

+ 0.34

V) — won't displace

H_{2}

. (4)

d^{5}

n^{2 +}

, F

e^{3 +}

) is extra stable.

Colour, Magnetism, Catalysis, Interstitials & Alloys

Colour from d–d transitions: In a partially filled d ion the d orbitals split in a ligand field; an electron absorbs visible light to jump between them (

d-d transition

) and the

complementary

colour is transmitted. Ions with

d^{0}

d^{10}

show no such transition and are colourless.

Ion (config)	Colour
$T i^{3 +} (d^{1})$	purple
$V^{3 +} (d^{2})$	green
$C r^{3 +} (d^{3})$	violet
$M n^{2 +} (d^{5})$	pale pink
$F e^{2 +} (d^{6})$	green
$C u^{2 +} (d^{9})$	blue
$d^{0}$ (S $c^{3 +}$ ), $d^{10}$ (Z $n^{2 +}$ )	colourless

Spin-only magnetic moment

μ = n (n + 2) BM

n =

number of unpaired electrons; more unpaired

e^{-}

⇒ more paramagnetic.

🎯 Exam · Worked moment

F e^{2 +} = 3 d^{6}

has

n = 4

unpaired

e^{-}

μ = 4 (4 + 2) = 24 = 4.90

BM. (

M n^{2 +} = d^{5}

n = 5 \Rightarrow 5.92

BM — the highest of the series.)

Catalytic activity

▸Arises from $variable oxidation states$ (easy electron transfer) and the ability to $adsorb$ reactants on the metal surface, providing a low-energy path.
▸ $Fe$ — Haber ( $N H_{3}$ ); $V_{2} O_{5}$ — Contact ( $H_{2} S O_{4}$ ); $Ni$ — hydrogenation; $Pd / Pt$ — many reactions.
▸ $F e^{3 +}$ catalyses the $I^{-} / S_{2} O_{8}^{2 -}$ reaction via an $F e^{3 +} / F e^{2 +}$ cycle.

★ Remember · Interstitial compounds

Small atoms (H, C, N, B) lodge in the holes of the metal lattice giving non-stoichiometric solids such as

TiC

M n_{4} N

F e_{3} H

. They are

very hard

, have high melting points and

retain metallic conductivity

— e.g. steel.

Complexes & alloys

▸ $Complex formation$ : small highly-charged ions with vacant d orbitals accept lone pairs from ligands, e.g. $[Fe (CN)_{6}]^{3 -}$ , $[Cu (N H_{3})_{4}]^{2 +}$ .
▸ $Alloys$ : similar atomic radii let transition metals substitute freely in one lattice, e.g. brass (Cu–Zn), bronze, steel.
▸Both rest on the same small-size + available- $d$ -orbital theme.

🚫 Examiner Trap · Examiner traps

(1) Colour is from

d-d transitions

—

d^{0}

c^{3 +}

) and

d^{10}

n^{2 +}

) are COLOURLESS. (2)

μ = n (n + 2)

BM counts

unpaired

electrons (n), spin-only. (3) Catalysis comes from variable oxidation states

+

surface adsorption. (4) Interstitial compounds (TiC) are hard, high-m.p., keep metallic conductivity.

Potassium Dichromate & Permanganate

Structures of dichromate ion as two CrO4 tetrahedra sharing a bridging oxygen with a Cr-O-Cr angle of 126 degrees and the tetrahedral permanganate ion, alongside their acidic-medium reduction half reactions and standard potentials — $C r_{2} O_{7}^{2 -}$ = two corner-sharing tetrahedra; $Mn O_{4}^{-}$ tetrahedral.

K_{2} C r_{2} O_{7}

— preparation

▸Roast chromite with $N a_{2} C O_{3}$ in air: $4 FeC r_{2} O_{4} + 8 N a_{2} C O_{3} + 7 O_{2} \to 8 N a_{2} Cr O_{4} + 2 F e_{2} O_{3} + 8 C O_{2}$ .
▸Acidify the yellow chromate to orange dichromate, then add KCl to crystallise $K_{2} C r_{2} O_{7}$ .

Chromate ⇌ dichromate (pH dependent)

2 Cr O_{4}^{2 -} + 2 H^{+} ⇌ C r_{2} O_{7}^{2 -} + H_{2} O

Acid ⇒ orange

C r_{2} O_{7}^{2 -}

; alkali ⇒ yellow

Cr O_{4}^{2 -}

Dichromate as oxidiser (acidic)

C r_{2} O_{7}^{2 -} + 14 H^{+} + 6 e^{-} \to 2 C r^{3 +} + 7 H_{2} O

E^{\circ} = + 1.33

V; orange → green. Used in volumetric estimation of

F e^{2 +}

and

I^{-}

KMn O_{4}

— preparation

▸Fuse pyrolusite with KOH and air/an oxidant: $2 Mn O_{2} + 4 KOH + O_{2} \to 2 K_{2} Mn O_{4} + 2 H_{2} O$ (green manganate).
▸Oxidise the manganate electrolytically (or by disproportionation): $3 Mn O_{4}^{2 -} + 4 H^{+} \to 2 Mn O_{4}^{-} + Mn O_{2} + 2 H_{2} O$ .

Permanganate as oxidiser (acidic)

Mn O_{4}^{-} + 8 H^{+} + 5 e^{-} \to M n^{2 +} + 4 H_{2} O

E^{\circ} = + 1.52

V; purple → colourless. In neutral/alkaline media it goes only to brown

Mn O_{2}

(

3 e^{-}

🎯 Exam · Structure & magnetism

Both

C r_{2} O_{7}^{2 -}

(two

Cr O_{4}

tetrahedra, Cr–O–Cr

12 6^{\circ}

) and

Mn O_{4}^{-}

(regular tetrahedron) have the metal in its

highest

state —

C r^{+ 6}

(

d^{0}

) and

M n^{+ 7}

(

d^{0}

) — so both are

diamagnetic

; their intense colour is a charge-transfer (O→M), not a d–d, transition.

⚠️ Watch out · Titration medium

Acidify

KMn O_{4}

titrations with

H_{2} S O_{4}

, never HCl —

C l^{-}

is oxidised to

C l_{2}

and gives a false (high) reading.

🚫 Examiner Trap · Examiner traps

(1) Chromate

⇌

dichromate is pH-controlled: acid

\to

orange C

r_{2} O_{7}^{2 -}

, alkali

\to

yellow CrO

_{4}^{2 -}

. (2) Acidify KMn

O_{4}

titrations with

H_{2} S O_{4}

, NEVER HCl (Cl

^{-}

oxidised

\to

l_{2}

, false reading). (3) C

r_{2} O_{7}^{2 -}

=

two corner-sharing Cr

O_{4}

tetrahedra (Cr–O–Cr

12 6^{\circ}

). (4) Both ions are

d^{0}

\Rightarrow

DIAMAGNETIC; colour is charge-transfer, not d–d.

Lanthanoids & the Lanthanoid Contraction

Lanthanoids (4f-block): The fourteen elements

Ce

(58) to

Lu

(71) following lanthanum, in which the

4 f

orbitals are progressively filled — general symbol

Ln

. Configuration

4 f^{1 - 14} 5 d^{0 - 1} 6 s^{2}

; the stable

L n^{3 +}

ions are simply

4 f^{n}

(

n = 1

–14).

Graph of Ln3+ ionic radius decreasing steadily from lanthanum to lutetium, with a side panel listing the cause and consequences including Zr approximately equal to Hf — Steady size decrease La→Lu and its consequences.

★ Remember · Lanthanoid contraction

The steady decrease in atomic and

L n^{3 +}

ionic radii from La to Lu. Cause: a

4 f

electron shields another

4 f

electron

poorly

, so the effective nuclear charge felt by the outer shell rises across the series.

Consequences

▸ $5 d$ atoms shrink to match the $4 d$ : $Zr (160) \approx Hf (159 pm)$ — second & third transition series resemble each other.
▸The Ln's are chemically alike and very $hard to separate$ .
▸Basic strength of hydroxides falls: $La (OH)_{3} > Lu (OH)_{3}$ (smaller ion, more covalent).

🎯 Exam · Oxidation states

+3 is the characteristic, most stable

state for all Ln. A few show

+ 2

+ 4

when that gives an empty, half-filled or full

4 f

C e^{4 +} (4 f^{0})

E u^{2 +} (4 f^{7})

T b^{4 +} (4 f^{7})

Y b^{2 +} (4 f^{14})

Ce4+ and Eu2+ — redox behaviour

▸ $C e^{4 +}$ is a strong $oxidant$ ( $E_{C e^{4 +} /C e^{3 +}}^{\circ} = + 1.74$ V), reverting to the stable $+ 3$ ; a useful analytical reagent (cerimetry).
▸ $E u^{2 +}$ and $Y b^{2 +}$ are strong $reductants$ , changing to the common $+ 3$ state.

General character & uses

▸Silvery-white soft metals that tarnish in air; most $L n^{3 +}$ are coloured and paramagnetic ( $f^{0}$ , $f^{14}$ colourless & diamagnetic).
▸React with water/acids giving $H_{2}$ , burn in $O_{2}$ to $L n_{2} O_{3}$ (basic).
▸ $Mischmetall$ (~95% Ln + ~5% Fe) → flints, tracer bullets; mixed Ln oxides catalyse petroleum cracking; used as TV/screen phosphors.

🚫 Examiner Trap · Examiner traps

(1)

+ 3

is the characteristic, most stable state for ALL lanthanoids. (2) Contraction is due to

poor 4 f shielding

(

Z_{eff} ↑

)

\Rightarrow

\approx

Hf, Ln's hard to separate. (3) C

e^{4 +}

(

4 f^{0}

) is a strong oxidant; E

u^{2 +}

(

4 f^{7}

)/Y

b^{2 +}

(

4 f^{14}

) are reductants. (4)

f^{0}

and

f^{14}

ions are colourless & diamagnetic.

Actinoids & f-Block Comparison

Actinoids (5f-block): The fourteen elements

Th

(90) to

Lr

(103) following actinium, in which the

5 f

orbitals fill (configuration

5 f^{1 - 14} 6 d^{0 - 1} 7 s^{2}

All are radioactive

; elements beyond uranium (transuranics) are synthetic.

🎯 Exam · Wider range of oxidation states

Actinoids show

+ 3

generally (like Ln), but the

early

members reach much higher states because

5 f

6 d

and

7 s

are close in energy: the maximum rises from

+ 4

(Th) to

+ 5

(Pa),

+ 6

(U) and

+ 7

(Np, Pu), then falls again.

★ Remember · Actinoid contraction

A gradual decrease in size across the series —

greater

from element to element than the lanthanoid contraction, because

5 f

electrons shield the nuclear charge even more poorly than

4 f

Why actinoid chemistry is more complex

▸ $5 f$ orbitals are $less buried$ than $4 f$ , so they take part in bonding more (more covalent character, more varied compounds).
▸Radioactivity and short half-lives of later members make them hard to study; many exist only in trace synthetic amounts.
▸Magnetic and spectral behaviour is harder to interpret than for the lanthanoids.

Lanthanoid vs actinoid summary

▸ $Configuration$ : $4 f$ filling (Ln) vs $5 f$ filling (An).
▸ $Oxidation states$ : Ln mainly $+ 3$ ; An show $+ 3$ plus many higher states.
▸ $Radioactivity$ : only $Pm$ among Ln; $all$ actinoids.
▸ $Reactivity$ : both reactive electropositive metals forming basic oxides/hydroxides.

⚠️ Watch out · Don't confuse the two contractions

Lanthanoid contraction makes

Zr \approx Hf

and governs the heavier d-block; actinoid contraction is the analogous,

steeper

shrink within the

5 f

series itself.

🚫 Examiner Trap · Examiner traps

(1)

All

actinoids are radioactive (only Pm among lanthanoids is). (2) Early actinoids reach much HIGHER states (U

+ 6

, Np/Pu

+ 7

) because

5 f, 6 d, 7 s

are close in energy. (3) Actinoid contraction is

greater

per element (

5 f

shields even worse than

4 f

). (4)

5 f

is less buried than

4 f

\Rightarrow

more covalent bonding.

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