Magnetic moment of `V(Z = 23),Cr(Z = 24),and Mn(Z= 25) are x,y,z `repectively hence

Options

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

Explanation

To determine the magnetic moments of Vanadium (V), Chromium (Cr), and Manganese (Mn), we will follow these steps:

### Step 1: Identify the Atomic Numbers and Electronic Configurations
- **Vanadium (V)** has an atomic number of 23. Its electronic configuration is:
\[ \text{V: } [Ar] 3d^3 4s^2 \]
- **Chromium (Cr)** has an atomic number of 24. Its electronic configuration is:
\[ \text{Cr: } [Ar] 3d^5 4s^1 \]
- **Manganese (Mn)** has an atomic number of 25. Its electronic configuration is:
\[ \text{Mn: } [Ar] 3d^5 4s^2 \]

### Step 2: Determine the Number of Unpaired Electrons
- For **Vanadium (V)**:
- The 3d subshell has 3 electrons (3 unpaired electrons).
- The 4s subshell has 2 electrons (paired).
- **Total unpaired electrons (n)** = 3.

- For **Chromium (Cr)**:
- The 3d subshell has 5 electrons (5 unpaired electrons).
- The 4s subshell has 1 electron (1 unpaired).
- **Total unpaired electrons (n)** = 5 + 1 = 6.

- For **Manganese (Mn)**:
- The 3d subshell has 5 electrons (5 unpaired electrons).
- The 4s subshell has 2 electrons (paired).
- **Total unpaired electrons (n)** = 5.

### Step 3: Calculate the Magnetic Moment
The magnetic moment (μ) can be calculated using the formula:
\[ \mu = \sqrt{n(n + 2)} \]

- For **Vanadium (V)**:
\[ \mu_V = \sqrt{3(3 + 2)} = \sqrt{3 \times 5} = \sqrt{15} \]

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

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

### Step 4: Compare the Magnetic Moments
Now we compare the values of the magnetic moments:
- \( \mu_V = \sqrt{15} \)
- \( \mu_{Cr} = \sqrt{48} \)
- \( \mu_{Mn} = \sqrt{35} \)

Since \( \sqrt{48} > \sqrt{35} > \sqrt{15} \), we can conclude:
- \( y > z > x \)
- Therefore, the order of magnetic moments is:
- \( y > z > x \)

### Final Answer
Thus, the magnetic moments of Vanadium, Chromium, and Manganese are in the order:
\[ y > z > x \]