Explain giving reasons: (i) Transition metals and many of their compounds show paramagnetic behaviour. (ii) Th

Exercises · 4.11

Q. Explain giving reasons:

(i) Transition metals and many of their compounds show paramagnetic behaviour.

(ii) The enthalpies of atomisation of the transition metals are high.

(iii) The transition metals generally form coloured compounds.

(iv) Transition metals and their many compounds act as good catalyst.

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Concept understanding — Magnetism and Color

Magnetism and Colour: An Intuitive First Look

You've probably noticed that some materials are magnetic (like iron) and others aren't (like wood). And you've seen that objects have different colours — a rose is red, the sky is blue. At first glance, these two properties seem completely unrelated. But at the deepest level, both magnetism and colour come from the same source: how electrons behave inside atoms.

Let's start with a simple picture.

The Intuition: Electrons as Tiny Magnets and Painters

Imagine an electron orbiting the nucleus of an atom. That moving charge is like a tiny loop of electric current — and any loop of current creates a magnetic field. So every electron is a microscopic magnet. In most materials, these tiny magnets point in random directions and cancel out. But in iron, they align, and the material becomes magnetic.

Now, colour. When light hits an atom, electrons can absorb some of its energy and jump to a higher orbit. The colour we see is the light that wasn't absorbed — the leftover wavelengths. Different atoms absorb different colours because their electrons have different "jump sizes" (energy levels).

So both magnetism and colour are about how electrons move and interact with their environment. One is about the direction of electron spin and orbit (magnetism), the other about the energy of electron jumps (colour).

The Precise Statement

Important

Magnetism and colour are both consequences of the electronic structure of atoms, but they arise from different aspects of electron behaviour:

Magnetism originates from the magnetic moments of electrons — their spin and orbital motion. A material is magnetic when these moments align cooperatively.
Colour originates from the absorption of specific wavelengths of light by electrons, which occurs when the photon energy matches the energy difference between two electron states.

How They Connect (and How They Don't)

The two phenomena are linked because they both depend on the arrangement of electrons in orbitals — the so-called electronic configuration. But they are not the same thing, and one does not cause the other.

Here's a table to make the distinction clear:

Property	Origin	What determines it?	Example
Magnetism	Electron spin and orbital motion	Unpaired electrons, crystal structure	Iron is magnetic because it has 4 unpaired electrons per atom
Colour	Electron transitions between energy levels	Energy gap between orbitals	Copper is reddish because its electrons absorb blue-green light

Note

A material can be magnetic and colourless (like pure iron — it's silvery, not colourful). A material can be brilliantly coloured and non-magnetic (like a ruby). The two properties are independent in most everyday cases.

The Deeper Link: Transition Metals

The most interesting connection appears in transition metals (elements like iron, cobalt, nickel, copper). These atoms have partially filled d orbitals. That partial filling does two things:

It leaves unpaired electrons, which can align to produce magnetism. …

Why this formula?

Magnetism and Color: Why the Key Formulas Hold

This is a fascinating intersection of physics and perception. The core idea is that color is not a property of light itself, but of our brain's interpretation of different wavelengths. Magnetism, in turn, can influence how these wavelengths are produced or absorbed.

Let's break down the key formulas and their why.

1. The Fundamental Link: Energy, Frequency, and Color

The most important formula connecting magnetism and color is the Planck-Einstein relation:

E = h \nu

Where:

$E$ = energy of a photon (light particle)
$h$ = Planck's constant ( $6.626 \times 10^{-34} \text{ J·s}$ )
$\nu$ = frequency of the light

Why does this hold?

Quantum nature of light: Light is not a continuous wave, but comes in discrete packets called photons.
Energy quantization: The energy of a photon is directly proportional to its frequency. Higher frequency means higher energy.
Magnetism's role: When an electron in an atom jumps from a higher energy level to a lower one, it emits a photon. The energy difference ( $\Delta E$ ) between these levels determines the photon's frequency:

\Delta E = h \nu

Color perception: Our eyes detect different frequencies as different colors. For example:
- Red light: $\nu \approx 4.3 \times 10^{14} \text{ Hz}$ (lower energy)
- Blue light: $\nu \approx 6.7 \times 10^{14} \text{ Hz}$ (higher energy)

Key insight: The color you see is determined by the energy gap between electron orbits. Magnetism can alter these energy gaps (via the Zeeman effect, see below).

2. The Zeeman Effect: How Magnetic Fields Split Colors

When a magnetic field is applied to an atom, a single spectral line (one color) splits into multiple lines. This is described by:

\Delta E = \mu_B \cdot B \cdot m_l

Where:

$\Delta E$ = energy shift of the spectral line
$\mu_B$ = Bohr magneton ( $9.274 \times 10^{-24} \text{ J/T}$ )
$B$ = magnetic field strength (in Tesla)
$m_l$ = magnetic quantum number (integer: $-l, ..., +l$ )

Why does this hold?

Electron as a tiny magnet: An electron orbiting a nucleus behaves like a tiny current loop, creating a magnetic dipole moment.
Energy in a magnetic field: This dipole moment interacts with an external magnetic field. The interaction energy depends on the orientation of the electron's orbit relative to the field.
Quantized orientations: The magnetic quantum number $m_l$ tells us which orientation is allowed. Each orientation has a slightly different energy.
Result: A single energy level splits into $2l+1$ sub-levels. Transitions between these sub-levels produce photons with slightly different energies — hence different colors appear.

Example: A sodium lamp emits yellow light. In a strong magnetic field, that yellow line splits into three closely spaced lines (normal Zeeman effect).

3. Faraday Rotation: Magnetic Field Twists Light's Color

When polarized light passes through a material in a magnetic field, its plane of polarization rotates. The rotation angle is:

\theta = V \cdot B \cdot d

Where:

$\theta$ = rotation angle (in radians)
$V$ = Verdet constant (material-specific, depends on wavelength)
$B$ = magnetic field strength
$d$ = path length through the material

Why does this hold?

Circular birefringence: In a magnetic field, the material has different refractive indices for left- and right-circularly polarized light.
Phase difference: These two components travel at different speeds, creating a phase difference.
Recombination: When they recombine, the resulting linear polarization is rotated. …

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The unique properties of transition metals — paramagnetism, high atomisation enthalpies, coloured compounds, and catalytic activity — all stem from the presence of partially filled d-orbitals. These orbitals give rise to unpaired electrons (paramagnetism), strong metallic bonding (high atomisation enthalpy), d-d electronic transitions (colour), and variable oxidation states with surface adsorption (catalysis).

Let’s unpack each statement one by one, connecting the behaviour to the underlying electronic structure.

(i) Transition metals and many of their compounds show paramagnetic behaviour.

Why this happens:

Paramagnetism arises from the presence of unpaired electrons. In transition metals, the $(n-1)d$ orbitals are being filled. These d-orbitals are five in number and, according to Hund’s rule, electrons occupy them singly before pairing. So, most transition metal ions (and many neutral atoms) have one or more unpaired electrons in their d-subshell.

Each unpaired electron behaves like a tiny magnet (it has a magnetic moment due to its spin). When an external magnetic field is applied, these atomic magnets align with the field, causing the substance to be attracted into the field — that’s paramagnetism.

Tip

The magnetic moment $\mu$ (in Bohr magnetons) can be estimated using the spin-only formula:

$\mu = \sqrt{n(n+2)}$

where $n$ is the number of unpaired electrons. For example, $\ce{Fe^{3+}}$ has $d^5$ configuration (all five electrons unpaired), so $\mu = \sqrt{5 \times 7} \approx 5.92$ BM — strongly paramagnetic.

Examples: $\ce{Cu^{2+}}$ (one unpaired electron), $\ce{Fe^{3+}}$ (five unpaired), $\ce{Mn^{2+}}$ (five unpaired).

Exceptions: $\ce{Zn^{2+}}$ and $\ce{Sc^{3+}}$ have $d^{10}$ and $d^0$ configurations respectively — no unpaired electrons — so they are diamagnetic (repelled by a magnetic field).

(ii) The enthalpies of atomisation of the transition metals are high.

Why this happens:

Atomisation enthalpy is the energy required to convert one mole of a metal in its solid state into isolated gaseous atoms. A high value means the metal atoms are strongly bonded to each other in the solid.

Transition metals have high atomisation enthalpies because of:

Strong metallic bonding — the bonding involves not just the s-electrons but also the d-electrons. The d-orbitals overlap with neighbouring atoms, contributing extra bonding strength.
High number of unpaired electrons — more unpaired d-electrons means more electrons available for metallic bonding. For example, vanadium ( $3d^3 4s^2$ , 515 kJ mol⁻¹ — the 3d maximum) and tungsten ( $5d^4 6s^2$ ) have very high atomisation enthalpies.
Trend across the series: Atomisation enthalpy rises from Sc, peaks where the most unpaired d-electrons actually take part in bonding (V in the 3d series; near the middle, Mo and W, in the heavier series), dips at Cr and sharply at Mn (their stable half-filled $3d^5$ holds electrons back), then falls towards the $d^{10}$ end. The peak corresponds to the maximum number of bonding-active unpaired d-electrons.

\Delta H_{\text{atom}} (\ce{Fe}) \approx 416 \ \text{kJ mol}^{-1}

Result: These high values explain why transition metals have high melting and boiling points, and why they are hard and dense.

(iii) The transition metals generally form coloured compounds.

Why this happens:

Colour in transition metal compounds is primarily due to d-d transitions. Here’s the chain of reasoning:

In a free transition metal ion, all five d-orbitals have the same energy (degenerate).
When the ion is placed in a crystal field (surrounded by ligands like water, chloride, etc.), the d-orbitals split into two sets of different energies — typically a lower-energy $t_{2g}$ set and a higher-energy $e_g$ set (in octahedral complexes).
The energy gap $\Delta$ (crystal field splitting energy) often falls in the visible region of the electromagnetic spectrum (roughly 1.5–3.0 eV).
Electrons in the lower set can absorb a photon of visible light and jump to the higher set. The colour we see is the complement of the absorbed colour. …

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Here is a clear, concept-first solution for the given questions, structured methodically for exam preparation.

Method: Electronic Configuration & Property Correlation

This method links the observable properties of transition metals directly to their unique electronic structure, specifically the presence of incompletely filled d-orbitals in their atoms or common ions.

(i) Paramagnetic Behaviour

Reason: Presence of unpaired electrons in the d-orbitals.

Step-by-step explanation:

Identify the cause: Paramagnetism arises from the spin of unpaired electrons. Each unpaired electron acts like a tiny magnet.
Apply to transition metals: Transition metals (elements in d-block) have an incompletely filled $(n-1)d$ subshell. In their elemental state or in many of their compounds (ions), these d-orbitals contain unpaired electrons.
Example: Consider $\ce{Fe^{3+}}$ (electronic configuration: $[\ce{Ar}]\,3d^5$ ). It has 5 unpaired electrons.
Conclusion: Because of these unpaired electrons, the ions are attracted into an external magnetic field, showing paramagnetic behaviour. The greater the number of unpaired electrons, the stronger the paramagnetism.

Key Result: Paramagnetism is directly proportional to the number of unpaired electrons in the d-subshell.

(ii) High Enthalpies of Atomisation

Reason: Strong metallic bonding due to a large number of unpaired electrons available for bonding.

Step-by-step explanation:

Define the term: Enthalpy of atomisation is the energy required to break the metallic lattice into individual atoms. A high value means strong bonding.
Identify the bonding: In transition metals, the metallic bond is formed by the delocalisation of electrons from both the s and d orbitals.
Explain the strength: Transition metals have a large number of unpaired d-electrons. These electrons participate in strong interatomic bonding. The more unpaired electrons available for delocalisation, the stronger the metallic bond.
Trend: This is why elements with several bonding-active unpaired d-electrons (V in the 3d series; Mo and W in the heavier series) have the highest enthalpies of atomisation — while Cr and especially Mn dip below the trend, their stable half-filled $3d^5$ electrons taking little part in metallic bonding (NCERT prints Mn at only 281 kJ mol⁻¹, the lowest of the series after Zn).
Conclusion: The strong metallic bonding, arising from the involvement of d-electrons, requires a large amount of energy to break, resulting in high enthalpies of atomisation.

Key Result: High atomisation enthalpy = strong metallic bond = many unpaired d-electrons contributing to bonding.

(iii) Formation of Coloured Compounds

Reason: d-d transition of electrons within the d-orbitals.

Step-by-step explanation:

Understand the condition: Colour is observed when a substance absorbs a specific wavelength of visible light and transmits the complementary colour.
Explain the mechanism (Crystal Field Theory): In a transition metal compound (e.g., $\ce{[Ti(H2O)6]^{3+}}$ ), the five d-orbitals are no longer equal in energy. They split into two sets (e.g., $t_{2g}$ and $e_g$ ) due to the electric field of surrounding ligands (like $\ce{H2O}$ ).
The d-d transition: The energy gap ( $\Delta$ ) between these split d-orbitals often corresponds to the energy of a photon in the visible light range.
The process: An electron from a lower energy d-orbital can absorb this photon and jump ("transition") to a higher energy d-orbital. …

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Here are the common mistakes students make on this specific question, broken down by sub-part, along with the correct reasoning and how to avoid each error.

General Mistake: Confusing "Magnetism" with "Colour"

Many students treat paramagnetism and colour as the same phenomenon. They are related (both involve d-electrons) but are not the same.

The Error: Saying "a compound is coloured because it is paramagnetic" or vice-versa.
The Fix:
- Paramagnetism is due to unpaired electrons (spin).
- Colour is due to d-d transitions (electron jumping between d-orbitals).
- A compound can be coloured yet diamagnetic — $KMnO_4$ is deep purple although $Mn^{7+}$ is $d^0$ with no unpaired electrons (its colour comes from charge transfer, not d-d transitions). Conversely, a paramagnetic ion can look almost colourless when its d-d transition is spin-forbidden (pale-pink $Mn^{2+}$ ) or lies outside the visible region.

(i) Paramagnetic Behaviour

Common Mistake 1: Vague "unpaired electrons" without linking to d-orbitals.

The Error: Simply writing "they have unpaired electrons" without explaining why transition metals have unpaired electrons.
How to Avoid: State the electronic configuration explicitly.
- Correct Reasoning: Transition metals have incompletely filled $(n-1)d$ orbitals. In many of their compounds (especially in +2 and +3 oxidation states), the d-orbitals are not fully filled. This results in one or more unpaired electrons.
- Key Formula: The magnetic moment $\mu = \sqrt{n(n+2)}$ BM (where $n$ = number of unpaired electrons). The presence of unpaired electrons causes the substance to be attracted into a magnetic field (paramagnetism).

Common Mistake 2: Forgetting exceptions (diamagnetic cases).

The Error: Stating all transition metal compounds are paramagnetic.
How to Avoid: Mention the exception: $Zn^{2+}$ ( $3d^{10}$ ), $Cu^+$ ( $3d^{10}$ ), and $Sc^{3+}$ ( $3d^0$ ) have no unpaired electrons and are diamagnetic (repelled by a magnetic field). The question asks for "many", not "all".

(ii) High Enthalpies of Atomisation

Common Mistake 1: Confusing "atomisation" with "ionisation".

The Error: Saying "high enthalpy of atomisation means it is hard to remove an electron."
How to Avoid: Define the term clearly.
- Atomisation: The enthalpy change when one mole of a solid metal is converted into gaseous atoms. It measures the strength of the metallic bond in the solid.
- Ionisation: The energy required to remove an electron from a gaseous atom.
- Correct Reasoning: Transition metals have high enthalpies of atomisation because of strong metallic bonding. This strong bonding arises from the large number of unpaired d-electrons that participate in metallic bonding, along with the small atomic size and high nuclear charge.

Common Mistake 2: Ignoring the trend within the series.

The Error: Giving a generic statement without noting the peak.
How to Avoid: Mention the real shape of the trend (Table 4.2): the enthalpy of atomisation rises from Sc (326 kJ mol $^{-1}$ ) to a maximum at V (515), then dips at Cr (397) and especially Mn (281) — their stable half-filled configurations contribute fewer unpaired electrons to metallic bonding — recovers through Fe–Ni (416–430), and finally falls drastically to Zn (126), where the fully filled $3d^{10}$ orbitals contribute no unpaired d-electrons to bonding.

(iii) Formation of Coloured Compounds

Common Mistake 1: Saying "colour is due to unpaired electrons".

The Error: This is the most frequent mistake. Colour and paramagnetism are correlated but not causally linked.
How to Avoid: Use the d-d transition explanation. …

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←Previous question4.10 — What are the different oxidation states exhibited by the lanthanoids?→Next question4.12 — What are interstitial compounds? Why are such compounds well known for…

Q.Explain giving reasons:

Concept understanding — Magnetism and Color

Magnetism and Colour: An Intuitive First Look

The Intuition: Electrons as Tiny Magnets and Painters

The Precise Statement

How They Connect (and How They Don't)

The Deeper Link: Transition Metals

Why this formula?

Magnetism and Color: Why the Key Formulas Hold

1. The Fundamental Link: Energy, Frequency, and Color

Why does this hold?

2. The Zeeman Effect: How Magnetic Fields Split Colors

Why does this hold?

3. Faraday Rotation: Magnetic Field Twists Light's Color

Why does this hold?

(i) Paramagnetic Behaviour of Transition Metals and Their Compounds

(i) Transition metals and many of their compounds show paramagnetic behaviour.

(ii) The enthalpies of atomisation of the transition metals are high.

(iii) The transition metals generally form coloured compounds.

Method: Electronic Configuration & Property Correlation

(i) Paramagnetic Behaviour

(ii) High Enthalpies of Atomisation

(iii) Formation of Coloured Compounds

General Mistake: Confusing "Magnetism" with "Colour"

(i) Paramagnetic Behaviour

(ii) High Enthalpies of Atomisation

(iii) Formation of Coloured Compounds

Q.Explain giving reasons:

(i) Transition metals and many of their compounds show paramagnetic behaviour.

(ii) The enthalpies of atomisation of the transition metals are high.

(iii) The transition metals generally form coloured compounds.

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