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 determine the correct representation of the relationship between atomic number (Z) and magnetic moment for 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 outer electronic configuration. The formula for calculating the magnetic moment is:
\[ \mu = \sqrt{n(n + 2)} \]
where \( n \) is the number of unpaired electrons.

### Step 2: Write the Electronic Configurations
For d-block elements, the outer electronic configuration can be represented as \((n-1)d^{x}ns^{1 \text{ or } 2}\). We will look at the electronic configurations starting from Scandium (Z = 21) to Zinc (Z = 30).

- **Z = 21 (Sc)**: Configuration: \( [Ar] 4s^2 3d^1 \) → 1 unpaired electron
- **Z = 22 (Ti)**: Configuration: \( [Ar] 4s^2 3d^2 \) → 2 unpaired electrons
- **Z = 23 (V)**: Configuration: \( [Ar] 4s^2 3d^3 \) → 3 unpaired electrons
- **Z = 24 (Cr)**: Configuration: \( [Ar] 4s^2 3d^5 \) → 6 unpaired electrons (due to half-filled stability)
- **Z = 25 (Mn)**: Configuration: \( [Ar] 4s^2 3d^5 \) → 5 unpaired electrons
- **Z = 26 (Fe)**: Configuration: \( [Ar] 4s^2 3d^6 \) → 4 unpaired electrons
- **Z = 27 (Co)**: Configuration: \( [Ar] 4s^2 3d^7 \) → 3 unpaired electrons
- **Z = 28 (Ni)**: Configuration: \( [Ar] 4s^2 3d^8 \) → 2 unpaired electrons
- **Z = 29 (Cu)**: Configuration: \( [Ar] 4s^2 3d^{10} \) → 1 unpaired electron
- **Z = 30 (Zn)**: Configuration: \( [Ar] 4s^2 3d^{10} \) → 0 unpaired electrons

### Step 3: Calculate the Magnetic Moments
Using the formula \( \mu = \sqrt{n(n + 2)} \), we can calculate the magnetic moment for each element:
- **Sc (Z=21)**: \( \mu = \sqrt{1(1 + 2)} = \sqrt{3} \)
- **Ti (Z=22)**: \( \mu = \sqrt{2(2 + 2)} = \sqrt{8} \)
- **V (Z=23)**: \( \mu = \sqrt{3(3 + 2)} = \sqrt{15} \)
- **Cr (Z=24)**: \( \mu = \sqrt{6(6 + 2)} = \sqrt{48} \)
- **Mn (Z=25)**: \( \mu = \sqrt{5(5 + 2)} = \sqrt{35} \)
- **Fe (Z=26)**: \( \mu = \sqrt{4(4 + 2)} = \sqrt{24} \)
- **Co (Z=27)**: \( \mu = \sqrt{3(3 + 2)} = \sqrt{15} \)
- **Ni (Z=28)**: \( \mu = \sqrt{2(2 + 2)} = \sqrt{8} \)
- **Cu (Z=29)**: \( \mu = \sqrt{1(1 + 2)} = \sqrt{3} \)
- **Zn (Z=30)**: \( \mu = 0 \)

### Step 4: Analyze the Trend
From the calculated values, we can observe that the magnetic moment increases initially as we move from Scandium to Chromium, reaches a peak, and then starts to decrease as we go towards Zinc.

### Step 5: Determine the Correct Graph
The correct graph representation would show an initial increase in magnetic moment, followed by a decrease after reaching a peak. Therefore, the graph that represents this trend is option D.

### Conclusion
The correct representation between atomic number (Z) and magnetic moment of d-block elements is option D, which shows an increase followed by a decrease in magnetic moment as atomic number increases.

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