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Q3.30(iii):
Assign the position of the element having outer electronic configuration (iii) ((n-2)f^{7}(n-1)d^{1}ns^{2}) for (n=6), in the periodic table.

Solution :

Step 1: Substitution of Principal Quantum Number

Given the general outer electronic configuration $(n-2)f^{7}(n-1)d^{1}ns^{2}$ where $n=6$. Substituting $n=6$ into the expression:

  • $(n-2)f^{7} = (6-2)f^{7} = 4f^{7}$
  • $(n-1)d^{1} = (6-1)d^{1} = 5d^{1}$
  • $ns^{2} = 6s^{2}$

The complete configuration of the valence and penultimate shells is $4f^{7}5d^{1}6s^{2}$. [Per the Aufbau Principle, electrons occupy orbitals in increasing order of energy].

Step 2: Determining the Full Electronic Configuration

To identify the element, we add the inner noble gas core. For $n=6$, the preceding noble gas is Xenon ($[Xe]$, $Z=54$).

Total electrons = $54 (\text{core}) + 7 (4f) + 1 (5d) + 2 (6s) = 64$.

The element with atomic number $Z=64$ is Gadolinium ($Gd$).

Step 3: Assigning Periodic Table Position

A. Block Assignment: Since the last electron enters the $f$-orbital (specifically the $4f$ subshell), the element belongs to the f-block [Per IUPAC classification of transition and inner-transition series].

B. Period Assignment: The principal quantum number $n$ corresponds to the period number. Since the outermost shell is $6s$, the element is in Period 6.

C. Group Assignment: All lanthanoids (elements with atomic numbers 57-71) are conventionally placed in Group 3 of the periodic table [Per the modern long-form periodic table structure].

Visual Representation of Electronic Energy Levels

4f (7e⁻) 5d (1e⁻) 6s (2e⁻) Configuration: [Xe] 4f⁷ 5d¹ 6s²

Summary of Data

Attribute Assignment
Atomic Number ($Z$) 64
Element Name Gadolinium ($Gd$)
Block f-block (Lanthanoid series)
Period 6
Group 3

Final Solution: The element is Gadolinium ($Gd$, $Z=64$), located in Period 6, Group 3, and belongs to the f-block (Lanthanoids).


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