(a) Account for the following: (i) Copper (I) compounds are white whereas Copper (II) compounds are coloured.

Question

Q. (a) Account for the following:

(i) Copper (I) compounds are white whereas Copper (II) compounds are coloured.

(ii) Chromates change their colour when kept in an acidic solution.

(iii) Zn, Cd, Hg are considered as d-block elements but not as transition elements.

(b) Calculate the spin-only moment of

Co^{2+}

(Z = 27) by writing the electronic configuration of Co and

Co^{2+}

(OR)

(a) Give three points of difference between lanthanoids and actinoids.

(b) Give reason and select one atom/ion which will exhibit asked property:

(i)

Sc^{3+}

Cr^{3+}

(Exhibit diamagnetic behaviour)

(ii) Cr or Cu (High melting and boiling point)

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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. …

(a) $Cu^+$ ( $d^{10}$ ) white vs $Cu^{2+}$ ( $d^9$ ) coloured; chromate↔dichromate with pH; Zn/Cd/Hg $d^{10}$ so not transition; $Co^{2+}$ ( $d^7$ , 3 unpaired) → $\mu=3.87$ BM.

(b) Ln vs An differ in oxidation states, radioactivity and complex formation; $Sc^{3+}$ ( $d^0$ ) diamagnetic; Cr > Cu in m.p./b.p.

(i) Cu(I) white, Cu(II) coloured

Colour needs a d–d transition, hence a partly filled d-subshell. $Cu^+$ is $[Ar]3d^{10}$ (completely filled) → no transition → white/colourless. $Cu^{2+}$ is $[Ar]3d^9$ (one vacancy) → an electron can be promoted within the split d-orbitals, absorbing visible light → coloured (e.g. blue $CuSO_4\cdot5H_2O$ ).

(ii) Chromates in acid

Chromate–dichromate is a pH-dependent equilibrium:

2CrO_4^{2-}\ (\text{yellow}) + 2H^+ \rightleftharpoons Cr_2O_7^{2-}\ (\text{orange}) + H_2O

Adding acid shifts it right (Le Chatelier) → yellow turns orange. Cr stays +6, so this is not a redox change.

(iii) Zn, Cd, Hg not transition elements

Their configurations are $3d^{10}4s^2$ , $4d^{10}5s^2$ , $5d^{10}6s^2$ ; in the common +2 ion the d-subshell is completely filled ( $d^{10}$ ). A transition element must have a partly filled d-subshell in its atom or a common ion, which these never do — so they are d-block but non-transition.

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Concept understanding — Actinoids

Actinoids: The Heavy, Radioactive Inner Transition Metals

Imagine you are walking through the periodic table, row by row. You know the lanthanoids — the 14 elements from cerium to lutetium that sit below the main table, where the 4f subshell is being filled. Now go one row lower. The elements that follow actinium (atomic number 89) are the actinoids: thorium (90) through lawrencium (103). Here, the 5f subshell is being filled.

The name comes from actinium, the first element of the series. But the real story begins with uranium and plutonium — the elements that made nuclear energy and atomic bombs possible. These are not just academic curiosities; they are the workhorses of nuclear physics.

The Precise Statement

Z=90

Why They Are Special

1. Radioactivity is the rule, not the exception. Every actinoid is radioactive. Some, like uranium-238, have half-lives comparable to the age of the Earth. Others, like lawrencium, exist for only seconds. This radioactivity is not a side effect — it is the defining property. It means their chemistry is often studied with trace amounts, using radiation detectors rather than test tubes.

2. Multiple oxidation states — more than you expect. Unlike the lanthanoids, which mostly stick to +3, the actinoids show a rich variety. Uranium, for example, exists as U $^{3+}$ , U $^{4+}$ , UO $_2^+$ (U $^{5+}$ ), and UO $_2^{2+}$ (U $^{6+}$ ). The early actinoids (Th, Pa, U, Np, Pu) are especially versatile because the 5f, 6d, and 7s orbitals are close in energy. As you move right, the +3 state becomes more stable — curium and beyond behave more like lanthanoids.

3. The actinoid contraction. As you go from Th to Lr, the nuclear charge increases by 14 protons. The 5f electrons are poor at shielding each other, so the effective nuclear charge felt by the outer electrons rises steadily. The result: ionic radii shrink smoothly across the series. This is exactly analogous to the lanthanoid contraction, and it has the same consequence — the chemistry of later actinoids becomes very similar to their lanthanoid counterparts, making separation difficult.

Tip

The actinoid contraction is why americium and curium are so hard to separate from the lanthanoids in nuclear waste. Their ionic radii are nearly identical.

A Quick Comparison with Lanthanoids

Property	Lanthanoids (4f)	Actinoids (5f)
Radioactivity	Mostly stable (except Pm)	All radioactive
Common oxidation state	+3 (strongly dominant)	+3, +4, +5, +6 (early ones)
5f vs 4f character	4f deeply buried, little bonding	5f more exposed, can participate in bonding

(a) $Cu^+$ ( $d^{10}$ ) white vs $Cu^{2+}$ ( $d^9$ ) coloured; chromate↔dichromate with pH; Zn/Cd/Hg $d^{10}$ so not transition; $Co^{2+}$ ( $d^7$ , 3 unpaired) → $\mu=3.87$ BM.

(b) Ln vs An differ in oxidation states, radioactivity and complex formation; $Sc^{3+}$ ( $d^0$ ) diamagnetic; Cr > Cu in m.p./b.p.

$Co^{2+}$ spin-only moment

Co (Z=27): $[Ar]3d^7 4s^2$ . Removing the two 4s electrons gives $Co^{2+}$ : $[Ar]3d^7$ , which has 3 unpaired electrons.

\mu = \sqrt{n(n+2)} = \sqrt{3(3+2)} = \sqrt{15} = 3.87\ \text{BM}

(Alternative) Part (a): Lanthanoids vs Actinoids — three differences

Property	Lanthanoids	Actinoids
Oxidation states	mainly +3 (few +2/+4)	wide range +3 to +7
Radioactivity	only Pm radioactive	all are radioactive
Complex formation	limited (4f buried, poorly shielded)	greater (5f more available)

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2026Set V11 markMCQ
$Q. Match the following given in List I with List II. List I (Elements) List II (Their maximum oxidation states) i) Thorium (Th) a) +7 ii) Protactinium (Pa) b) +6 iii) Lawrencium (Lr) c) +3 iv) Uranium (U) d) +5 v) Plutonium (Pu) e) +4 Choose the correct option :$
(a) i – e, ii – d, iii – a, iv – b, v – c
(b) i – e, ii – d, iii – c, iv – b, v – a
(c) i – b, ii – a, iii – c, iv – e, v – d
(d) i – b, ii – e, iii – c, iv – d, v – a
›Reveal solutionSolution
Matching each actinoid to its maximum oxidation state gives Th– $+4$ , Pa– $+5$ , Lr– $+3$ , U– $+6$ , Pu– $+7$ , i.e. option (b).

Early actinoids show a rise in maximum oxidation state as the number of available $5f/6d$ electrons increases, peaking around U–Np–Pu, then falling again toward the heavier members (which behave much like lanthanoids with a stable $+3$ state).

i) Thorium (Th): maximum oxidation state $= +4$ → (e)

ii) Protactinium (Pa): maximum oxidation state $= +5$ → (d) …
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CBSE 2025Set 56/4/11 markMCQ
$Q. For the following question, two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) given below. Assertion (A) : Cuprous salts are diamagnetic. Reason (R) : Cuprous ion has completely filled 3d-orbitals. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true.$
›Reveal solutionSolution
Cuprous salts are diamagnetic because the Cu⁺ ion has a completely filled 3d¹⁰ configuration, leaving no unpaired electrons. Both Assertion and Reason are true, and the Reason correctly explains the Assertion — so the answer is (A).

Why magnetism and electron configuration matter

Magnetic behaviour in transition metal compounds comes down to one thing: unpaired electrons. A substance with any unpaired electrons is paramagnetic (attracted to a magnetic field); one with all electrons paired is diamagnetic (weakly repelled). So to judge whether cuprous salts are diamagnetic, we need to know the electron configuration of the cuprous ion, Cu⁺.

Copper’s atomic number is 29. The neutral atom has the configuration $[\text{Ar}]\,3d^{10}4s^1$ — that one 4s electron is what gives copper its typical +1 and +2 oxidation states. When copper loses one electron to form Cu⁺, it loses that 4s electron first (not a 3d electron, because the 4s orbital is higher in energy once occupied). So Cu⁺ becomes $[\text{Ar}]\,3d^{10}$ .

That’s a completely filled d-subshell. All ten 3d electrons are paired up in five orbitals. No unpaired electrons means diamagnetic.

Now let’s check the Assertion and Reason carefully.

Assertion (A): “Cuprous salts are diamagnetic.”

True. As we just saw, Cu⁺ has no unpaired electrons. Every cuprous salt — CuCl, Cu₂O, Cu₂S, etc. — contains Cu⁺, so the salt as a whole is diamagnetic. (The anion doesn’t contribute unpaired electrons either, so the whole compound is diamagnetic.)

Reason (R): “Cuprous ion has completely filled 3d-orbitals.”

True. The configuration is $3d^{10}$ , which is indeed completely filled.

Is (R) the correct explanation of (A)? …
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CBSE 2025Set ANNUAL1 markMCQ
$Q. Element of actinoid series is -$
(a) Thorium
(b) Cerium
(c) Cadmium
(d) Chromium
›Reveal solutionSolution
Thorium (Th, Z = 90) belongs to the actinoid series; the other three options are not actinoids.

Actinoids are the 14 elements from Th (Z=90) to Lr (Z=103) that follow actinium, in which the 5f orbitals are progressively filled.

Checking each option:

Thorium (Z=90): an actinoid.

Cerium (Z=58): a lanthanoid (4f block), not an actinoid. …
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CBSE 2024Set B1 mark
$Q. Write True or False: Lanthanoids is more reactive than actinoids.$
›Reveal solutionSolution

Because of their larger size and lower ionisation enthalpies (and comparable energies of 5f, 6d, 7s orbitals), actinoids are more reactive than lanthanoids, especially in the finely divided state.

Lanthanoids (4f series) are comparatively less reactive, tarnishing slowly in air, while actinoids (5f series) — especially the early actinoids like thorium, uranium, plutonium — are much more reactive: they combine readily with most non-metals, tarnish rapidly, and some (like plutonium) are pyrophoric in powdered form. This higher reactivity of actinoids is attributed to their larger atomic/ionic radii and t …

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CBSE 2023Set ANNUAL1 markMCQ
$Q. The maximum oxidation state exhibited by actinides is:$
(a) +7
(b) +5
(c) +4
(d) +8
›Reveal solutionSolution

Actinides can show oxidation states from +3 up to a maximum of +7, because the 5f, 6d and 7s electrons are close in energy and all can participate in bonding.

+3 is the most common and stable oxidation state throughout the actinide series (like +3 is typical for lanthanides), but because the 5f orbitals extend further from the nucleus than the 4f orbitals of lanthanides and are less effectively shielded, more of the outer electrons of an actinide atom can be involved in bonding. This lets some early actinides reach higher oxidation states than lanthanides ever d …

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CBSE 2023Set ANNUAL1 mark
$Q. Why do actinoids show larger number of oxidation states as compared to the lanthanoids ?$
›Reveal solutionSolution

The near-equal energies of 5f/6d/7s in actinoids let more electrons participate in bonding than the more energetically separated 4f/5d/6s orbitals of lanthanoids allow.

In lanthanoids, the 4f orbitals are deeply buried beneath the filled 5s and 5p subshells and are well shielded from the nucleus; they lie considerably lower in energy than the 5d and 6s orbitals. As a result, 4f electrons rarely take part in bonding, and lanthanoids show an overwhelmingly dominant +3 oxidation state, with only occasional +2/+4 states (when they give a specially stable f⁰, f⁷ or f¹⁴ configuration).

…

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CBSE 2022Set E1 markMCQ
$Q. Which of the following is not an actinide ?$
(a) Curium
(b) Californium
(c) Uranium
(d) Terbium
›Reveal solutionSolution

Terbium belongs to the lanthanide (4f) series; curium, californium and uranium are actinides (5f).

Actinides are the 5f-series elements (Z = 90-103), which include uranium (92), curium (96) and californium (98).

…

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CBSE 2022Set ANNUAL1 markMCQ
$Q. Trivalent ion of which of the following lanthanide metals is colourless ?$
(a) La
(b) Ce
(c) Pr
(d) Nd
›Reveal solutionSolution
La³⁺ has an empty 4f subshell, so it has no f-electrons to undergo f–f transitions and is colourless; the other listed ions all carry unpaired f-electrons and are coloured.

Colour in lanthanide ions arises mainly from f–f electronic transitions, which require partially-filled f orbitals. Checking the configurations of $M^{3+}$ :

La³⁺: $[Xe]4f^0$ — no f-electrons → colourless.

Ce³⁺: $[Xe]4f^1$ — coloured (pale).

Pr³⁺: $[Xe]4f^2$ — coloured.

Nd³⁺: $[Xe]4f^3$ — coloured. …
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CBSE 2020Set 56/3/11 mark
$Cu^{2+}$
›Reveal solutionSolution
The colour of transition metal ions arises from d-d electronic transitions, which require partially filled d-orbitals. $Cu^{2+}$ has a $3d^9$ configuration (one unpaired electron) allowing such transitions, while $Zn^{2+}$ has a $3d^{10}$ configuration (completely filled d-subshell) with no vacant d-orbital for electron excitation, making it colourless.

The Concept: Colour and Electronic Structure

Colour in transition metal compounds is a direct consequence of their electronic configuration. When white light falls on a substance, certain wavelengths are absorbed, and the complementary colour is transmitted or reflected. For a transition metal ion in solution, the absorption typically occurs in the visible region due to d-d transitions — electrons jumping from a lower-energy d-orbital to a higher-energy d-orbital within the same subshell.

This is only possible when the d-subshell is partially filled. If the d-orbitals are completely empty ( $d^0$ ) or completely filled ( $d^{10}$ ), no d-d transition can occur because there is either no electron to excite or no vacant orbital to receive it. Such ions appear colourless.

Step-by-Step Reasoning

Electronic configuration of the atoms

Copper (Cu, atomic number 29): $[Ar]\,3d^{10}4s^1$

Zinc (Zn, atomic number 30): $[Ar]\,3d^{10}4s^2$

Formation of the +2 ions

When forming $Cu^{2+}$ , the atom loses the 4s electron and one 3d electron:

$Cu^{2+}: [Ar]\,3d^9$

When forming $Zn^{2+}$ , the atom loses both 4s electrons:

$Zn^{2+}: [Ar]\,3d^{10}$

d-orbital occupancy in aqueous solution

In aqueous solution, water molecules act as ligands and create a crystal field around the metal ion. For octahedral complexes (common for both ions in water), the five d-orbitals split into two sets: the lower-energy $t_{2g}$ set ( $d_{xy}, d_{xz}, d_{yz}$ ) and the higher-energy $e_g$ set ( $d_{z^2}, d_{x^2-y^2}$ ).

$Cu^{2+}$ ( $3d^9$ ): Nine electrons occupy the d-orbitals. The configuration is $(t_{2g})^6(e_g)^3$ , with one unpaired electron in the $e_g$ level. There is a vacant orbital in the $e_g$ set, and an electron from the filled $t_{2g}$ set can be excited into it by absorbing visible light. This d-d transition gives $Cu^{2+}$ its characteristic blue colour in aqueous solution.

$Zn^{2+}$ ( $3d^{10}$ ): All five d-orbitals are completely filled. There is no vacant d-orbital to accept an excited electron. The only possible electronic transitions would involve much higher energy levels (like 4s or 4p), which require ultraviolet light, not visible. Hence, no visible light is absorbed, and the solution appears colourless. …
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CBSE 2019Set ANNUAL1 mark
$Q. What is the most common oxidation state of the Actinoids?$
›Reveal solutionSolution

Like the lanthanoids, actinoids show a wide range of oxidation states, but $+3$ is the most common/characteristic one.

Actinoids exhibit a greater range of oxidation states than lanthanoids (owing to the closer energies of $5f$ , $6d$ and $7s$ orbitals), but the most common and characteristic oxidation state throughout the series, as with the lanthanoids …

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CBSE 2018Set ANNUAL1 mark
$Q. Write name and symbol of one transurenic element.$
›Reveal solutionSolution

A transuranic element is any element with atomic number greater than 92 (uranium); Neptunium (Np, Z = 93) is one example.

Elements with atomic number beyond that of uranium (Z = 92) are called transuranic (or transuranium) elements. They are all synthetic/man-made, produced in nuclear reactors or particle accelerators by bombarding heavy nuclei with neutrons or light nuclei, and all are radioactive. Examples include Neptunium (Np, Z = 93), Plutonium (Pu, Z = 94), …

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	List I (Elements)		List II (Their maximum oxidation states)
i)	Thorium (Th)	a)	+7
ii)	Protactinium (Pa)	b)	+6
iii)	Lawrencium (Lr)	c)	+3
iv)	Uranium (U)	d)	+5
v)	Plutonium (Pu)	e)	+4

Q.(a) Account for the following:

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) Cu(I) white, Cu(II) coloured

(ii) Chromates in acid

(iii) Zn, Cd, Hg not transition elements

Concept understanding — Actinoids

Actinoids: The Heavy, Radioactive Inner Transition Metals

The Precise Statement

Why They Are Special

A Quick Comparison with Lanthanoids

Co2+Co^{2+}Co2+ spin-only moment

(Alternative) Part (a): Lanthanoids vs Actinoids — three differences

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$Co^{2+}$ spin-only moment

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