which of the following graph is correct representation between atomic number (Z) and magnetic moment of d-block elements? [outer electronic configuration: `(n-1)d^(x)ns^(1 or 2)`]

Options

A.
B.
C.
D.

Explanation

To solve the question regarding the correct representation of the relationship between atomic number (Z) and magnetic moment of d-block elements, we can follow these steps:

### Step 1: Understand the Concept of Magnetic Moment
The magnetic moment (μ) of an atom is related to the number of unpaired electrons (n) in its d-orbitals. The formula for calculating the magnetic moment is given by:
\[ \mu = \sqrt{n(n + 2)} \]
where \( n \) is the number of unpaired electrons.

### Step 2: Analyze the Electron Configuration of d-block Elements
The outer electronic configuration of d-block elements is given as \((n-1)d^x ns^{1 \text{ or } 2}\). This means that the d-block elements fill their d-orbitals after the s-orbitals of the previous shell.

### Step 3: Determine the Number of Unpaired Electrons
For d-block elements:
- When filling the d-orbitals, the first five electrons (d1 to d5) will each occupy a separate orbital, leading to an increase in the number of unpaired electrons (1 to 5).
- As we continue to fill the d-orbitals (d6 to d10), pairing begins to occur, which decreases the number of unpaired electrons.

### Step 4: Observe the Trend
- From \( d^1 \) to \( d^5 \), the number of unpaired electrons increases, and thus the magnetic moment increases.
- From \( d^6 \) to \( d^{10} \), the number of unpaired electrons decreases, leading to a decrease in the magnetic moment.

### Step 5: Identify the Correct Graph
Given the trend of increasing magnetic moment with increasing atomic number up to \( d^5 \) and then decreasing from \( d^6 \) to \( d^{10} \), the correct graph will show an initial rise followed by a fall.

### Conclusion
The correct representation of the relationship between atomic number (Z) and magnetic moment for d-block elements is represented by option D, which shows an increase in magnetic moment with atomic number up to a certain point, followed by a decrease.

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