Magnetic moment of `Cr(Z=24), Mn^+(Z=25)` and`Fe^(2+)(Z=26)` are x,y,z. They are in order

Options

A. `x lt y lt z`
B. `x=y lt z`
C. `z lt x= y`
D. x=y=z

Answer

To determine the magnetic moments of Chromium (Cr), Manganese ion (Mn⁺), and Iron ion (Fe²⁺), we will follow these steps:

### Step 1: Determine the electronic configurations
- **Chromium (Cr, Z=24)**: The electronic configuration is \( \text{Ar} \, 3d^5 \, 4s^1 \).
- **Manganese ion (Mn⁺, Z=25)**: The electronic configuration is \( \text{Ar} \, 3d^5 \, 4s^0 \) (since it loses one electron from the 4s orbital).
- **Iron ion (Fe²⁺, Z=26)**: The electronic configuration is \( \text{Ar} \, 3d^6 \, 4s^0 \) (it loses two electrons, one from the 4s and one from the 3d orbital).

### Step 2: Count the number of unpaired electrons
- **For Chromium (Cr)**:
- Configuration: \( 3d^5 \, 4s^1 \)
- Unpaired electrons: 6 (5 in \( 3d \) and 1 in \( 4s \))

- **For Manganese ion (Mn⁺)**:
- Configuration: \( 3d^5 \)
- Unpaired electrons: 5 (all 5 electrons in \( 3d \) are unpaired)

- **For Iron ion (Fe²⁺)**:
- Configuration: \( 3d^6 \)
- Unpaired electrons: 4 (the arrangement in \( 3d \) will have 4 unpaired electrons)

### Step 3: Use the formula for magnetic moment
The formula for the magnetic moment (\( \mu \)) is given by:
\[ \mu = \sqrt{n(n + 2)} \]
where \( n \) is the number of unpaired electrons.

- **For Chromium (Cr)**:
- \( n = 6 \)
- \( \mu_{Cr} = \sqrt{6(6 + 2)} = \sqrt{6 \times 8} = \sqrt{48} \)

- **For Manganese ion (Mn⁺)**:
- \( n = 5 \)
- \( \mu_{Mn^+} = \sqrt{5(5 + 2)} = \sqrt{5 \times 7} = \sqrt{35} \)

- **For Iron ion (Fe²⁺)**:
- \( n = 4 \)
- \( \mu_{Fe^{2+}} = \sqrt{4(4 + 2)} = \sqrt{4 \times 6} = \sqrt{24} \)

### Step 4: Compare the magnetic moments
Now we can compare the magnetic moments:
- \( \mu_{Cr} = \sqrt{48} \)
- \( \mu_{Mn^+} = \sqrt{35} \)
- \( \mu_{Fe^{2+}} = \sqrt{24} \)

### Step 5: Order the magnetic moments
From the calculations:
- \( \mu_{Cr} > \mu_{Mn^+} > \mu_{Fe^{2+}} \)

Thus, the order of magnetic moments is:
- \( x > y > z \)
where \( x = \mu_{Cr} \), \( y = \mu_{Mn^+} \), and \( z = \mu_{Fe^{2+}} \).

### Final Answer:
The order of magnetic moments is \( x > y > z \).

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