Q.(a) Answer the following questions:
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🔒 Start your 14-day free trial to unlock the full solution →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
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 |
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=hν
Where:
- E = energy of a photon (light particle)
- h = Planck's constant (6.626×10−34 J⋅s)
- ν = 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 (ΔE) between these levels determines the photon's frequency:
ΔE=hν
- Color perception: Our eyes detect different frequencies as different colors. For example:
- Red light: ν≈4.3×1014 Hz (lower energy)
- Blue light: ν≈6.7×1014 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:
ΔE=μB⋅B⋅ml
Where:
- ΔE = energy shift of the spectral line
- μB = Bohr magneton (9.274×10−24 J/T)
- B = magnetic field strength (in Tesla)
- ml = 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 ml 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:
θ=V⋅B⋅d
Where:
- θ = 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. …
(a) The key idea is that ionisation enthalpies and atomisation enthalpies in the first transition series (Sc to Zn) are governed by electronic configurations — particularly half-filled and fully-filled d subshell stability.
(i) Highest second ionisation enthalpy: After losing one electron, the element with a stable d5 or d10 configuration resists further loss. For the second IE, Cu (3d104s1) loses one 4s electron to become 3d10 (stable). Removing a second electron from this stable d10 requires very high energy. …
The key idea is to use electronic configurations and periodic trends across the first transition series (Sc–Zn). For (a), the highest second ionisation enthalpy belongs to Cu, the highest third to Zn, and the lowest enthalpy of atomisation to Zn. For (b), the metal in M(CO)5 is Fe (as Fe(CO)5), and in MO3F it is Mn (as MnO3F).
(a) Ionisation enthalpies and enthalpy of atomisation in the first transition series
The first transition series runs from Sc (atomic number 21) to Zn (30). The trends in ionisation enthalpies and enthalpy of atomisation are governed by the stability of half-filled and fully-filled d subshells, and by the strength of metallic bonding.
1. Highest second ionisation enthalpy
Second ionisation enthalpy (IE2) is the energy needed to remove an electron from the M+ ion. For most elements, IE2 is larger than IE1, but the jump is especially large when the M+ ion has a stable configuration.
- Consider Cu (3d104s1). After losing one electron, Cu+ becomes 3d10 — a completely filled d subshell, which is very stable. Removing a second electron from this stable d10 core requires a lot of energy.
- Compare with Zn (3d104s2): Zn+ is 3d104s1, not as stable as Cu+. So Cu has the highest IE2 in the series.
A common mistake is to think Zn has the highest IE2 because it has the highest IE1. But IE2 depends on the stability of the monovalent cation, not the neutral atom. Cu+ (d10) is exceptionally stable.
2. Highest third ionisation enthalpy
Third ionisation enthalpy (IE3) is the energy to remove an electron from M2+.
- Zn2+ has configuration 3d10 — again a fully filled d subshell. Removing a third electron from this stable d10 core is extremely difficult.
- No other M2+ in the series has a d10 configuration (e.g., Cu2+ is d9, Ni2+ is d8). So Zn has the highest IE3.
3. Lowest enthalpy of atomisation
Enthalpy of atomisation (ΔHatom) reflects the strength of metallic bonding. Across the series, metallic bonding depends on the number of unpaired d electrons available for bonding.
- Zn has a 3d104s2 configuration — all d electrons are paired. This leads to weak metallic bonding (Zn is relatively volatile, with a low melting point).
- In contrast, elements like Cr (3d54s1) or Mn (3d54s2) have many unpaired electrons and stronger bonding.
- Hence, Zn has the lowest enthalpy of atomisation.
A quick way to remember: Zn is the odd one out — it has the highest IE3 (due to d10 in M2+) and the lowest atomisation enthalpy (due to no unpaired d electrons). Cu has the highest IE2 because Cu+ is d10.
(b) Identifying the metal in given compounds
4. Carbonyl M(CO)5 …
Method: Electronic Configuration & Periodic Trends Analysis
This method uses the electronic configuration of elements in the first transition series (Sc to Zn) and applies periodic trends in ionisation enthalpy and enthalpy of atomisation.
(a) Step-by-step reasoning
(i) Highest second ionisation enthalpy
Step 1: Write the general outer configuration for first transition series:
3d1−104s1−2
Step 2: Second ionisation enthalpy is high when the M+ ion has a stable configuration (half-filled or fully filled d subshell).
- Zn (3d104s2): Zn→Zn+ (removes 4s1), then Zn+→Zn2+ removes one 3d electron — breaking a fully filled 3d10 shell. This requires very high energy.
Answer: Zinc (Zn)
(ii) Highest third ionisation enthalpy
Step 1: Third ionisation enthalpy is highest when the M2+ ion has a stable configuration.
- Zn (3d104s2): Zn2+ has 3d10 (fully filled). Removing one more electron breaks this stable configuration → very high third IE.
Answer: Zinc (Zn)
(iii) Lowest enthalpy of atomisation
Step 1: Enthalpy of atomisation depends on metallic bond strength, which increases with number of unpaired d-electrons.
- Zn has 3d104s2 — no unpaired electrons → weak metallic bonding → lowest atomisation enthalpy.
Answer: Zinc (Zn)
(b) Identify the metal and justify
(i) Carbonyl M(CO)5
Step 1: Apply 18-electron rule for stable carbonyls.
Each CO donates 2 electrons. For M(CO)5:
M contributes x valence electrons, 5×2=10 from CO. …
(a) Ionisation Enthalpies & Atomisation Enthalpy
(i) Highest second ionisation enthalpy
Concept:
Second ionisation enthalpy (IE2) is the energy needed to remove an electron from a +1 cation. The highest IE2 occurs when the +1 cation has a stable electronic configuration — removing another electron would break that stability.
- For first transition series (Sc to Zn), the +1 state is rarely stable.
- The element with the highest IE2 is Zinc (Zn).
- Reason: Zn⁺ has configuration 3d104s1. Removing one more electron gives Zn²⁺ (3d10), which is stable. However, the jump from 3d104s1 to 3d10 is not the highest second ionisation enthalpy in the series.
Correct answer:
Copper (Cu) has the highest IE2 in the first transition series.
- Cu⁺ has configuration 3d10 (completely filled d-subshell — very stable).
- Removing an electron from this stable 3d10 to get Cu²⁺ (3d9) requires a lot of energy.
- So IE2 of Cu is the highest.
Common mistake: Students often pick Zn because Zn²⁺ is stable. But Zn⁺ (3d104s1) is not as stable as Cu⁺ (3d10). The stability of the +1 cation determines IE2.
How to avoid:
Always check the electronic configuration of the +1 ion. The more stable it is, the higher the IE2.
(ii) Highest third ionisation enthalpy
Concept:
Third ionisation enthalpy (IE3) is the energy to remove an electron from a +2 cation. The highest IE3 occurs when the +2 cation has a stable configuration.
- Zinc (Zn) has the highest IE3.
- Zn²⁺ has configuration 3d10 (completely filled — very stable).
- Removing one more electron gives Zn³⁺ (3d9), breaking that stable filled subshell.
- This requires maximum energy.
Common mistake: Students sometimes pick Mn (because Mn²⁺ is half-filled stable). But Mn²⁺ (3d5) is stable, so IE3 is not the highest — it’s actually lower than Zn.
How to avoid:
Remember: Filled subshell (d10) is more stable than half-filled (d5). So Zn²⁺ > Mn²⁺ in stability → Zn has higher IE3.
(iii) Lowest enthalpy of atomisation
Concept:
Enthalpy of atomisation (ΔHatom) is the energy required to convert the metal into isolated gaseous atoms. It depends on metallic bond strength.
- In the first transition series, Zinc (Zn) has the lowest ΔHatom.
- Zn has no unpaired electrons in its ground state (3d104s2).
- Metallic bonding is weaker because there are no unpaired d-electrons to contribute to bonding.
Common mistake: Students think Mn (half-filled) has lowest atomisation enthalpy. But Mn has five unpaired electrons → strong metallic bonding → higher ΔHatom.
How to avoid:
More unpaired d-electrons → stronger metallic bond → higher atomisation enthalpy. Zn has zero unpaired electrons → weakest bonding → lowest ΔHatom.
(b) Identify the metal and justify
(i) Carbonyl M(CO)5
Concept:
Metal carbonyls follow the 18-electron rule (effective atomic number rule). For a neutral carbonyl M(CO)5:
- Each CO donates 2 electrons.
- Total electrons from CO = 5×2=10.
- Metal must contribute 8 electrons to reach 18.
- So the metal must have 8 valence electrons in its neutral state.
Which first transition series metal has 8 valence electrons?
- Configuration: 3d64s2 → Iron (Fe).
- Fe(CO)5 is a well-known stable compound.
Common mistake: Students guess Ni or Co. But Ni(CO)4 is tetrahedral (18e⁻), and Co₂(CO)₈ is dimeric. Only Fe gives a stable mononuclear pentacarbonyl.
How to avoid: …
- COMEDK 2026Set 2026-M1 markMCQQ.Which one of the following species will impart colour to an aqueous solution? (A) Cr3+ (B) Zn2+ (C) Ti4+ (D) Cu+
›Reveal solutionSolution
Colour in aqueous solution arises from d–d transitions in transition-metal ions with partially filled d-orbitals. Among the options, only Cr³⁺ has an incomplete d-subshell (d³), so it is the species that imparts colour.
The key concept is crystal field theory and d–d transitions. For a transition-metal ion to appear coloured in solution, it must have at least one unpaired electron in its d-orbitals, allowing it to absorb visible light by promoting an electron from a lower-energy d-orbital to a higher-energy one. Ions with completely filled (d¹⁰) or empty (d⁰) d-subshells cannot undergo such transitions and are typically colourless.
Let’s examine each option:
-
Cr³⁺ – Chromium in the +3 oxidation state has the electron configuration [Ar] 3d³. The d-subshell is partially filled (three d-electrons). This allows d–d transitions, so Cr³⁺ solutions (e.g., CrCl₃) are typically violet or green. This will impart colour.
-
Zn²⁺ – Zinc in the +2 state has the configuration [Ar] 3d¹⁰. The d-subshell is completely filled. No d–d transitions are possible, and Zn²⁺ solutions are colourless. No colour.
-
Ti⁴⁺ – Titanium(IV) has lost all four valence electrons, giving [Ar] (no d-electrons). The d-subshell is empty (d⁰). No d–d transitions possible; Ti⁴⁺ solutions are colourless. No colour. …
-
- COMEDK 2025Set 2025-M1 markMCQQ.Choose the correct statement. (A) Ionic compounds of Sc3+ and Cu+are coloured because of d−d electronic transitions (B) The order in which the paramagnetic nature of the 4 cations Cr2+,Mn2+,V2+ and Fe2+ vary is V2+<Cr2+=Mn2+<Fe2+ (C) As the oxidation number of the transition element increases, the ionic nature decreases and the oxides show acidic nature predominantly (D) The metal Cobalt has the electronic configuration [Ar]3 d5 in the +3 oxidation state
›Reveal solutionSolution
The key is to evaluate each statement using principles of transition-metal chemistry: d–d transitions require partially filled d-orbitals, paramagnetism depends on unpaired electrons, ionic character and acidity relate to oxidation state, and Co³⁺ has a 3d⁶ configuration. Only statement (C) is correct.
Concept and Intuition
Transition-metal compounds exhibit colour, paramagnetism, and variable oxidation states due to their partially filled d-orbitals. Each statement here tests a specific concept:
- Colour from d–d transitions requires at least one d-electron and an empty d-orbital to allow excitation.
- Paramagnetic strength is proportional to the number of unpaired electrons.
- Higher oxidation states increase covalent character (Fajan’s rules) and make oxides more acidic.
- The electron configuration of an ion is found by removing electrons from the neutral atom’s configuration, starting with the 4s orbital.
Step-by-step analysis
-
Statement (A):
- Sc³⁺ has the configuration [Ar] (no d-electrons). Without any d-electrons, d–d transitions are impossible.
- Cu⁺ has configuration [Ar] 3d¹⁰ (full d-subshell). A full d-subshell means no empty d-orbital to accept an excited electron, so d–d transitions cannot occur.
- Therefore, neither ion can be coloured via d–d transitions. Statement (A) is false.
-
Statement (B):
- Determine the number of unpaired electrons for each ion (all are 2+ ions of first-row transition metals):
- V²⁺: [Ar] 3d³ → 3 unpaired electrons.
- Cr²⁺: [Ar] 3d⁴ → 4 unpaired electrons (high-spin, as in aqueous complexes).
- Mn²⁺: [Ar] 3d⁵ → 5 unpaired electrons.
- Fe²⁺: [Ar] 3d⁶ → 4 unpaired electrons (high-spin).
- Paramagnetic nature increases with number of unpaired electrons. So the order should be: V²⁺ (3) < Cr²⁺ (4) = Fe²⁺ (4) < Mn²⁺ (5).
- The given order is V²⁺ < Cr²⁺ = Mn²⁺ < Fe²⁺, which incorrectly places Mn²⁺ equal to Cr²⁺ and Fe²⁺ as the most paramagnetic.
- Statement (B) is false.
- Determine the number of unpaired electrons for each ion (all are 2+ ions of first-row transition metals):
-
Statement (C): …
- COMEDK 2024Set 2024-E1 markMCQQ.The Lanthanoid ion which would form coloured compounds is -------------. Atomic numbers: Yb=70,Lu=71,Pr=59,La=57 (A) Yb2+ (B) La3+ (C) Lu3+ (D) Pr3+
›Reveal solutionSolution
Colour in lanthanoid ions arises from f–f transitions, which require at least one unpaired electron in the 4f subshell. Among the given ions, only Pr³⁺ (4f²) has unpaired electrons, so it forms coloured compounds.
Concept & Intuition
Lanthanoid ions often display beautiful colours in solution or in solids. The colour comes from electronic transitions within the partially filled 4f orbitals. These f–f transitions are Laporte-forbidden but become weakly allowed due to vibronic coupling, giving pale but distinct colours. The key requirement is that the ion must have at least one unpaired electron in its 4f subshell. If the 4f subshell is empty (4f⁰) or completely full (4f¹⁴), no such transitions are possible, and the ion is colourless.
Let’s check each option.
-
Yb²⁺ (Ytterbium, atomic number 70)
- Neutral Yb: [Xe] 4f¹⁴ 6s²
- Yb²⁺ loses the two 6s electrons: [Xe] 4f¹⁴
- 4f subshell is completely full → no unpaired electrons → colourless.
-
La³⁺ (Lanthanum, atomic number 57)
- Neutral La: [Xe] 5d¹ 6s²
- La³⁺ loses the 5d and both 6s electrons: [Xe] 4f⁰
- 4f subshell is empty → no unpaired electrons → colourless.
-
Lu³⁺ (Lutetium, atomic number 71)
- Neutral Lu: [Xe] 4f¹⁴ 5d¹ 6s²
- Lu³⁺ loses the 5d and both 6s electrons: [Xe] 4f¹⁴
- Again, 4f subshell is full → no unpaired electrons → colourless.
-
Pr³⁺ (Praseodymium, atomic number 59)
- Neutral Pr: [Xe] 4f³ 6s²
- Pr³⁺ loses the two 6s electrons and one 4f electron: [Xe] 4f² …
-
- KCET 2023Set D-21 markMCQQ.Which of the following is CORRECT with respect to melting point of a transition element? (A) V > Cr (B) Cr > Mn (C) Mn > Fe (D) Ti > V
›Reveal solutionSolution
Recall the NCERT melting-point trend across the 3d series and test each inequality; Mn's anomalously low melting point makes Cr > Mn the robust correct statement.
Step 1 — The concept behind the trend
In a transition metal, the strength of metallic bonding depends on how many unpaired d-electrons are available to take part in interatomic (covalent-like) bonding on top of the metallic sea. Bonding strength — and hence melting point — therefore rises to a maximum near the middle of the series and falls off towards the end as d-electrons begin to pair up.
Step 2 — The data (NCERT, 3d series, ∘C)
Ti 1677V 1917Cr 1903Mn 1244Fe 1535
Step 3 — The Mn anomaly (the point of the question)
Manganese has the configuration 3d54s2. Its half-filled d-subshell is exceptionally stable, so those five electrons are reluctant to delocalise into the metallic bond. With fewer electrons effectively contributing to bonding, Mn's metallic bonding is weak and its melting point (1244∘C) is far below both its neighbours Cr (1903∘C) and Fe (1535∘C). This dip is the famous irregularity in the melting-point curve.
Step 4 — Test each option
- (B) Cr > Mn: 1903>1244 — TRUE, and by a very large margin (this is the Mn anomaly). …
- COMEDK 2023Set 2023-M1 markMCQQ.Ti2+ is purple while Ti4+ is colourless because (A) Ti2+ has 3d2 configuration (B) Ti4+ has 3d2 configuration (C) Ti2+ is very small cation when compared to Ti2+ and hence, doesn't absorb any radiation (D) There is no crystal field effect in Ti4+
›Reveal solutionSolution
Colour in transition-metal ions comes from d–d electronic transitions, which require partially filled d orbitals. Ti2+ (3d2) has d electrons and is coloured (purple); Ti4+ (3d0) has none and is colourless.
Titanium: Ti (Z=22) =[Ar]3d24s2.
- Ti2+: remove the two 4s electrons ⇒[Ar]3d2. With two d electrons, d–d transitions are possible, absorbing visible light and imparting the purple colour. …
- KCET 2021Set B-21 markMCQQ.Which one of the following is correct for all elements from Sc to Cu? (A) The lowest oxidation state shown by them is +2 (B) 4s orbital is completely filled in the ground state (C) 3d orbital is not completely filled in the ground state (D) The ions in +2 oxidation states are paramagnetic.
›Reveal solutionSolution
Every +2 ion from Sc2+ (3d1) to Cu2+ (3d9) carries unpaired 3d electrons, so all are paramagnetic — option (D).
Test each statement across Sc–Cu (the 3d series).
(A) False — Sc's lowest common state is +3 and Cu shows +1, so +2 is not the lowest for every element.
(B) False — in Cr [Ar]3d54s1 and Cu [Ar]3d104s1 the 4s orbital holds only one electron.
(C) False — Cu is [Ar]3d104s1, so its 3d subshell is completely filled.
(D) True — the two 4s electrons are lost first, so each +2 ion is 3dn: …
- KCET 2021Set B-21 markMCQQ.The property of the alkaline earth metals that increases with their atomic number is (A) Ionisation enthalpy (B) Electronegativity (C) Solubility of their hydroxide in water (D) Solubility of their sulphate in water
›Reveal solutionSolution
Only hydroxide solubility rises down group 2; ionisation enthalpy, electronegativity and sulphate solubility all fall.
Step 1 — The governing principle for solubility trends
Whether an ionic solid dissolves depends on the competition between two quantities:
ΔHsoln=ΔHhydration−ΔHlattice
Both lattice and hydration enthalpies decrease as the cation gets bigger down the group. Which one falls faster decides the trend — and that depends on the size of the anion:
- With a small anion (OH−, F−), the lattice enthalpy is very sensitive to the cation size, so it falls faster than the hydration enthalpy ⇒ solubility increases down the group.
- With a large anion (SO42−, CO32−), the lattice enthalpy is dominated by the big anion and barely changes; the hydration enthalpy of the cation falls faster ⇒ solubility decreases down the group.
Step 2 — Apply it to each option
(C) Hydroxides. OH− is a small anion, so the first case applies:
Be(OH)2<Mg(OH)2<Ca(OH)2<Sr(OH)2<Ba(OH)2
Solubility (and hence basic strength) increases with atomic number. Mg(OH)2 is only sparingly soluble (milk of magnesia), while Ba(OH)2 is appreciably soluble and a strong base. ✓ This is the property that increases. …
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