Mn²⁺ ⇒ 3d⁵ contains 5 unpaired electrons
n = 5,
\( \sqrt{n(n+ 2)} \) BM
\(= \sqrt{5(5+ 2)} = \sqrt{35} = 5.92 BM\)

Cr ⇒ [Ar]3d⁵4s¹

(i) It is used as a strong oxidizing agent
(ii) It is used in dyeing and printing.
(iii) It used in leather tanneries for chrome tanning.
(iv) It is used in quantitative analysis for the estimation of iron compounds and iodides.

(i) When potassium dichromate is heated with any chloride salt in the presence of Conc. H₂SO₄, orange red vapours of chromyl chloride (CrO₂CI₂) is evolved.
(ii) This reaction is used to confirm the presence of chloride ion in inorganic qualitative analysis

(iii) The chromyl chloride vapours are dissolved in sodium hydroxide solution and then acidified with acetic acid and treated with lead acetate. A yellow precipitate of lead chromate is obtained

(i) Transition elements have a tendency to form coordination compounds with a species that has an ability to donate an electron pair to form a co-ordinate covalent bond.
(ii) Transition metal ions are small and highly charged and they have vacant low energy orbitals to accept an electron pair donated by other groups. Due to these properties, transition metals form large number of complex.
(iii) Examples: [Fe(CN)₆]^4-, [Co(NH₃)₆]³⁺, etc.

(i) Fe³⁺ - electronic configuration - [Ar] 3d⁵
(ii) It has exactly half-filled stable electronic configuration.
(iii) Fe²⁺ - electronic configuration -[Ar]3d⁶
(iv) It has only partially filled d-orbitals.
Hence Fe³⁺ is more stable than Fe²⁺.

IUPAC defines transition metal as an element whose atom has an incomplete d-sub shell or which can give rise to cations with an incomplete d-sub shell. They occupy the central position of the periodic table, between s and p-block elements.
Examples: Fe, Cu, Ag, Au

(i) According to Hume-Rothery rule to, form a substitute alloy the difference between the atomic radii of solvent and solute is less than 15%.
(ii) Both the solvent and solute must have the same crystal structure and valence and their electro negativity difference must be close to zero.

A mixture of TiCl₄ and trialkyl aluminium is used for polymerization.

Standard electrode potential is the value of the standard emf of a cell in which molecular hydrogen under standard pressure (1 atm) and temperature (273K) is oxidised to solvate protons at the electrode.

(i) Transition metals have number of unpaired electron. They are involved in metallic bonding. Hence they show high melting point.
(ii) As we move from left to right along the transition metal series melting point first increases reach a maximum value and then decreases as the d-electrons pair up and become less available for bonding.

Electronic configuration of Ce⁴⁺ = [Xe] 4f⁰5d⁰6s⁰
Electronic configuration of Co²⁺ = [Ar]3d⁷

An interstitial compound or alloy is a compound that is formed when small atoms like hydrogen, boron, carbon or nitrogen are trapped in the interstitial holes in a metal lattice. They are usually non-stoichiometric compounds. Transition metals form a number of interstitial compounds such as TiC, ZrH_1.92, Mn₄N etc.
Properties of interstitial compound
(i) They are hard and show electrical and thermal conductivity.
(ii) They have high melting points higher than those of pure metals.
(iii) Transition metal hydrides are used as powerful reducing agents 
(iv) Metallic carbides are chemically inert.

(i) The compounds of Cu²⁺ are coloured as it has one free electron its valence shell which absorb I radiation of visible region and get excited to emit its complementary colour.
(ii) Zn has no free electron it has fully filled shells. Due to extra stable orbitals electron can't be excited by radiations of visible light, hence its compounds are colourless.

The oxidation states of 4d metals vary from +3 for Y to +8 for Ru and Os.
The highest oxidation state of 4d elements are found in their compounds with the higher electronegative elements like O, F & Cl.
Example: In RuO₄, OsO₄ & WCl₆
The oxidation state of Ru and Os is +8.
The oxidation state of W is +6.
Generally in going down a group, a stability of higher oxidation state increases while that of lower oxidation state decreases.
4d series (5^th period) - Yttrium to Cadmium (10 elements)

(i) It oxidises ferrous salts to ferric salts.
 Cr₂O₇^2- + 6Fe²⁺+ 14H⁺ ⟶ 2Cr³⁺ + 6Fe³⁺ + 7H₂O
(ii) It oxidises iodide ions to iodine
Cr₂O₇^2- + 6I^-+ 14H⁺ ⟶ 2Cr³⁺ + 3I₂ + 7H₂O
(iii) It oxidises sulphide ion to sulphur
Cr₂O₇^2- + 3S^2-+ 14H⁺ ⟶ 2Cr³⁺ + 3S + 7H₂O
(iv) It oxidises sulphur dioxide to sulphate ion
Cr₂O₇^2- + 3SO₂+ 2H⁺ ⟶ 2Cr³⁺ + 3SO₄^2- + H₂O
(v) It oxidises stannous salts to stannic salt
 Cr₂O₇^2- + 3Sn²⁺ + 14H⁺ ⟶ 2Cr³⁺ + 3Sn⁴⁺ + 7H₂O
(vi) It oxidises alcohols to acids
2K₂Cr₂O₇ + 8H₂SO₄ + 3CH₃CH₂OH ⟶ 2K₂SO₄ +2Cr₂(SO₄)₃+ 3CH₃COOH + 11H₂O
(vii) It oxidises oxalic acid to CO2
2MnO₄^- + 5(COO)^2- + 6H⁺ ⟶ 2Mn²⁺+ 10CO₂ + 8H₂O
(viii) It oxidises iodide ions to iodine
2MnO4^- + 10I^- + 16H⁺ ⟶ 2Mn²⁺+ 5I₂+ 8H₂O
(ix) It oxidises sulphide ion to sulphur
2MnO₄^- + 5S^2-+ 16H⁺ ⟶ 2Mn²⁺+ 5S + 8H₂O
(x) It oxidises nitrites to nitrates
 2MnO₄^- + 5NO^2- + 6H⁺ ⟶ 2Mn²⁺+ 5NO₃^- + 3H₂O
(xi) It oxidises alcohols to aldehydes.
 2KMnO₄ + 3H₂SO₄ + 5CH₃CH₂OH ⟶ 2K₂SO₄ + 2MnSO₄ + 5CH₃CHO + 8H₂O
(xii) It oxidises sulphite to sulphate
2MnO₄^- + 5SO₃^2- + 6H⁺ ⟶ 2Mn²⁺ + 5SO₄^2- + 3H₂O

(i) Only the ions that have unpaired electrons in d- orbital and in which d - d transition is possible will be coloured.
(ii) The ions in which d - orbitals are empty or completely filled will be colourless as no d -d transition is possible in those configurations.
(iii) From the above ions, it can be easily observed that only Sc³⁺ has an empty d - orbital and Cu⁺ has completely filled d-orbitals.
(vi) All other ions, except Sc³⁺ and Cu⁺, will be coloured in aqueous solution because of d - d transition.