Compare the general characteristics of the first series of the transition metals with those of the second and

Exercises · 4.35

Q. Compare the general characteristics of the first series of the transition metals with those of the second and third series metals in the respective vertical columns. Give special emphasis on the following points:

(i) electronic configurations

(ii) oxidation states

(iii) ionisation enthalpies and

(iv) atomic sizes.

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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 first transition series (3d) differs from the second (4d) and third (5d) series mainly due to lanthanoid contraction, which nearly equalises 4d and 5d atomic sizes and makes 5d metals more inert. The 3d series shows more variable oxidation states, lower ionisation enthalpies, and smaller atomic radii, while 4d and 5d metals have higher ionisation enthalpies, more stable higher oxidation states, and nearly identical atomic sizes within a group.

The Big Picture: Why the 3d Series is Special

The transition metals are defined by the filling of the inner d-orbitals. The first series (Sc to Zn, 3d¹⁻¹⁰) is the first time these orbitals are populated. The second (Y to Cd, 4d¹⁻¹⁰) and third (La to Hg, 5d¹⁻¹⁰) series come after the 4f and 5f lanthanoids and actinoids, respectively. This ordering creates a crucial effect: the lanthanoid contraction. As we fill the 4f orbitals across the lanthanide series (Ce to Lu), the nuclear charge increases, but the 4f electrons shield poorly. This causes a steady, significant contraction in atomic and ionic radii. When we then start the 5d series, the atoms are already much smaller than expected — almost the same size as their 4d counterparts. This single fact ripples through all four properties we need to compare.

Step-by-Step Comparison

1. Electronic Configurations

The general configuration is $[noble\,gas]\,(n-1)d^{1-10}\,ns^{1-2}$ , but there are important exceptions.

First series (3d): Configurations are mostly $3d^{1-8}\,4s^2$ , but Cr and Cu break the pattern:
- Cr: $[Ar]\,3d^5\,4s^1$ (half-filled d-subshell stability)
- Cu: $[Ar]\,3d^{10}\,4s^1$ (fully filled d-subshell stability)
- Others: e.g., Fe $[Ar]\,3d^6\,4s^2$ , Ni $[Ar]\,3d^8\,4s^2$
Second series (4d): Similar exceptions occur, but more frequently because the energy gap between 4d and 5s is smaller than between 3d and 4s.
- Nb: $[Kr]\,4d^4\,5s^1$ (not $4d^3\,5s^2$ )
- Mo: $[Kr]\,4d^5\,5s^1$ (like Cr)
- Ru: $[Kr]\,4d^7\,5s^1$ (not $4d^6\,5s^2$ )
- Rh: $[Kr]\,4d^8\,5s^1$
- Pd: $[Kr]\,4d^{10}\,5s^0$ (unique — complete d-subshell, no s-electron)
- Ag: $[Kr]\,4d^{10}\,5s^1$ (like Cu)
Third series (5d): The lanthanoid contraction makes the 5d and 6s orbitals very close in energy, so exceptions are even more common. Also, the 4f orbitals are filled before 5d begins.
- Pt: $[Xe]\,4f^{14}\,5d^9\,6s^1$ (not $5d^8\,6s^2$ )
- Au: $[Xe]\,4f^{14}\,5d^{10}\,6s^1$ (like Cu, Ag)
- W: $[Xe]\,4f^{14}\,5d^4\,6s^2$ (regular)
- Hg: $[Xe]\,4f^{14}\,5d^{10}\,6s^2$ (regular)

Tip

The trend is: as we go down a group, exceptions to the $(n-1)d^x\,ns^2$ rule become more common. The 5d series has the most exceptions because the 5d and 6s orbitals are nearly degenerate.

2. Oxidation States

First series (3d): These metals show a wide range of oxidation states, often with +2 and +3 being most stable. The +2 state arises from losing the two 4s electrons; higher states involve d-electrons. For example:
- Mn: +2, +3, +4, +6, +7
- Fe: +2, +3
- Co: +2, +3
- Ni: +2 (most stable), +3, +4
- Cu: +1, +2
- The highest state reached in the 3d series is +7 (Mn); no 3d metal reaches +8 — even iron manages only +6, in the rare ferrate ion FeO₄²⁻.
Second and third series (4d and 5d): Higher oxidation states become more stable. For example:
- Mo and W: +6 is very stable (MoO₃, WO₃)
- Tc and Re: +7 is stable (TcO₄⁻, ReO₄⁻)
- Ru and Os: +8 is possible (RuO₄, OsO₄) — OsO₄ is a well-known oxidising agent.
- The +2 state is less common and less stable for the heavier metals — for platinum, for instance, the +4 state is at least as prominent as +2. The key point is that higher states become more accessible down the group.

Watch out

A common mistake is to think that all transition metals show +2 and +3 states equally. In the 4d and 5d series, the +2 state is often unstable or not observed at all (e.g., Zr⁴⁺ is the only common state; Zr²⁺ is rare). The stability of high oxidation states increases down the group.

Why? The 4d and 5d orbitals are more diffuse and can better accommodate the loss of many electrons. Also, the lanthanoid contraction makes the 5d metals more compact, increasing the effective nuclear charge and stabilising high oxidation states.

3. Ionisation Enthalpies

Ionisation enthalpy (IE) is the energy required to remove an electron. For transition metals, we consider the sum of successive IEs (IE₁ + IE₂ + ...) to reach a given oxidation state.

First series (3d): IE values are relatively low. For example:
- IE₁ for Sc: 631 kJ/mol, for Zn: 906 kJ/mol
- IE₂ for Fe: 1561 kJ/mol, for Cu: 1958 kJ/mol
- The trend across the series is a general increase, but with irregularities due to half-filled and fully filled d-subshells (e.g., Cr has a lower IE₁ than Mn because Cr has a half-filled 3d⁵ 4s¹ configuration, making it easier to remove the 4s electron).
Second and third series (4d and 5d): IE values are higher than for the 3d series. For example:
- IE₁ for Mo: 684 kJ/mol, for W: 770 kJ/mol (compare to Cr: 653 kJ/mol)
- IE₂ for Mo: 1560 kJ/mol, for W: 1700 kJ/mol
- The increase is due to the lanthanoid contraction: the 5d metals have smaller atomic radii and higher effective nuclear charge, so electrons are held more tightly.

The trend in ionisation enthalpy down a group: IE increases from 3d to 4d, but 4d and 5d are very close (sometimes 5d is slightly higher, sometimes slightly lower). This is a direct consequence of the lanthanoid contraction nearly equalising the sizes of 4d and 5d atoms.

4. Atomic Sizes

Atomic radius decreases across a period and increases down a group. But here, the lanthanoid contraction creates a striking anomaly. …

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Method: Periodic Trend Analysis Across Transition Series

This method compares properties across the three transition series by identifying horizontal trends (within a series) and vertical trends (down a group), then linking them to underlying principles like shielding, nuclear charge, and orbital energies.

Steps

1. Electronic Configurations

First series (3d): General configuration: $[Ar]\, 3d^{1-10}\, 4s^{1-2}$ Example: Sc: $[Ar]\, 3d^1\,4s^2$ ; Zn: $[Ar]\, 3d^{10}\,4s^2$
Second series (4d): $[Kr]\, 4d^{1-10}\, 5s^{1-2}$
Third series (5d): $[Xe]\, 4f^{1-14}\, 5d^{1-10}\, 6s^{1-2}$ (Note: Lanthanide contraction affects 5d series)

Key point: Down a group, the $(n-1)d$ orbital fills similarly, but lanthanide contraction (poor shielding by 4f electrons) makes 4d and 5d radii nearly equal.

2. Oxidation States

First series: Show +2 and +3 as common states; higher states (+4 to +7) are less stable (e.g., Mn shows +2 to +7, but +7 is strongly oxidising).
Second & third series: Higher oxidation states become more stable (e.g., Mo in +6, W in +6 are stable; Ru in +8 exists).
Reason: 4d and 5d orbitals are more diffuse, allowing better overlap with ligands and stabilising high oxidation states.

Trend: Down a group, maximum oxidation state increases in stability.

3. Ionisation Enthalpies

General trend: First series → generally lower ionisation enthalpies than the 5d metals (3d-vs-4d comparisons are mixed element by element). Second & third series → higher values due to greater nuclear charge and poorer shielding.
Note: although the lanthanide contraction makes 4d and 5d atoms nearly the same size, the 5d metals' first ionisation enthalpies are generally higher — the intervening, poorly shielding 4f electrons raise the effective nuclear charge.

Key result:

$\Delta H_{ionisation}: 3d \lesssim 4d < 5d$ (as a broad trend — NCERT's emphasised point is that the 5d values are the distinctly higher ones)

4. Atomic Sizes

Across a series: Atomic radius decreases slowly (poor shielding by d-electrons).
Down a group: …

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Here is a breakdown of the common mistakes students make when comparing the first, second, and third series of transition metals, along with strategies to avoid them.

The Core Concept: The Lanthanoid Contraction

Before we list the mistakes, you must understand the single most important concept that governs all the differences: the Lanthanoid Contraction.

What it is: As we move across the Lanthanide series (Ce to Lu), the 4f orbitals are filled. The 4f electrons have a very poor shielding effect.
The Consequence: The effective nuclear charge ( $Z_{eff}$ ) experienced by the outer electrons increases dramatically. This pulls the entire electron cloud inward, causing a steady and significant decrease in atomic and ionic radii across the lanthanides.
The Ripple Effect: This contraction is so powerful that the atomic radii of the 4d and 5d transition metals in the same vertical group become almost identical. For example, Zr (4d) and Hf (5d) have nearly the same size.

Mistake #1: Assuming Electronic Configurations are Perfectly Regular

The Mistake:

Students write the electronic configurations as perfectly predictable (e.g., $3d^4 4s^2$ for Cr, $3d^9 4s^2$ for Cu). They also fail to see the pattern of irregularities across the three series.

The Correct Understanding & How to Avoid:

The Rule: The $(n-1)d$ and $ns$ orbitals are very close in energy. Half-filled ( $d^5$ ) and fully-filled ( $d^{10}$ ) subshells have extra stability.
The First Series Anomalies:
- Cr: Expected $3d^4 4s^2$ , Actual $3d^5 4s^1$ (to achieve a half-filled d-subshell).
- Cu: Expected $3d^9 4s^2$ , Actual $3d^{10} 4s^1$ (to achieve a fully-filled d-subshell).
The Second & Third Series: These irregularities are more frequent in the 4d series — the $(n-1)d$ $(n - 1) d$ and $ns$ $n s$ energies lie even closer, so many 4d metals deviate (Nb, Mo, Ru, Rh, Pd, Ag).
- Exception: Pd (Palladium) in the 4d series has the anomalous configuration $4d^{10} 5s^0$ , not $4d^8 5s^2$ .
How to Avoid: Memorize the exceptions for Cr, Cu, and Pd. For the rest, assume the regular $ns^2 (n-1)d^{1-10}$ pattern. Don't assume the 2nd and 3rd series behave exactly like the 1st.

Mistake #2: Claiming Higher Oxidation States are "Unstable" in the 1st Series

The Mistake:

Students say that higher oxidation states (like +7 for Mn) are unstable in the first series but stable in the second and third series. This is vague and often wrong.

The Correct Understanding & How to Avoid:

The Truth: Higher oxidation states are common in all three series. The key difference is stability in different chemical environments.
The Trend:
- 1st Series (3d): Higher states (e.g., Mn(VII) in $MnO_4^-$ , Cr(VI) in $Cr_2O_7^{2-}$ ) are strongly oxidising. They are stable in oxo-anions but easily reduced.
- 2nd & 3rd Series (4d & 5d): Higher states (e.g., Mo(VI) in $MoO_4^{2-}$ , W(VI) in $WO_4^{2-}$ , Ru(VIII) in $RuO_4$ ) are more stable and less oxidising.
Why? The 4d and 5d orbitals are more diffuse and can better accommodate the high positive charge. The Lanthanoid contraction also makes the 5d elements more compact, stabilising the higher state.
How to Avoid: Don't say "higher states don't exist in the 1st series." Say: "Higher oxidation states are more stable in the 2nd and 3rd series. In the 1st series, they are strong oxidising agents and less stable in aqueous solutions."

Mistake #3: Ignoring the Trend in Ionisation Enthalpies

The Mistake:

Students simply state that ionisation enthalpy increases across a period and decreases down a group, without explaining the anomalous jump in the 1st series or the near-equality in the 2nd and 3rd series.

The Correct Understanding & How to Avoid:

The General Trend: Ionisation enthalpy increases across a period (due to increasing $Z_{eff}$ ) and decreases down a group (due to increasing atomic size and shielding).
The 1st Series Anomaly: The increase is not smooth. There are small dips due to the stability of half-filled and fully-filled configurations.
- Example: the values do not rise smoothly — Cr's $\Delta_i H_1$ (653 kJ mol⁻¹) sits barely above V's (650) despite the higher nuclear charge, and Ni's (736) is actually lower than Co's (758). NCERT attributes these irregularities to the varying stability of the different 3d configurations.
The 2nd vs. 3rd Series Anomaly: Due to the Lanthanoid contraction, the atomic sizes of the 4d and 5d elements are nearly the same. Therefore, their ionisation enthalpies are also very similar.
- Example: The first ionisation enthalpy of Zr (4d) and Hf (5d) are almost identical. …

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Q.Compare the general characteristics of the first series of the transition metals with those of the second and third series metals in the respective vertical columns. Give special emphasis on the following points:

The Big Picture: Why the 3d Series is Special

Step-by-Step Comparison

1. Electronic Configurations

2. Oxidation States

3. Ionisation Enthalpies

4. Atomic Sizes

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