Question

Spin only magnetic moment is same for which of the following ions?
A. T³⁺
B. Cr²⁺
C. Mn²⁺
D. Fe²⁺
E. Se³⁺
Choose the most appropriate answer from the options given below

• A. B and D only
• B. A and E only
• C. B and C only
• D. A and D only

Answer 1

The Correct Option is A

1. Magnetic moment is calculated as:

$\mu = \sqrt{n(n + 2)} \, \text{BM}$,

where $n$ is the number of unpaired electrons.

2. For $Cr^{2+}$ ($d^4$) and $Fe^{2+}$ ($d^6$), $n = 4$. Both ions have the same spin-only magnetic moment:

$\mu = \sqrt{4(4 + 2)} = 4.90 \, BM$.

Answer 2

Step 1: Recall the Formula for Magnetic Moment 

The spin-only magnetic moment (\( \mu \)) is given by:

$$ \mu = \sqrt{n(n+2)} $$

where \( n \) is the number of unpaired electrons. The magnetic moment depends only on the number of unpaired electrons in the ion.

Step 2: Analyze the Given Ions

A. \( Ti^{3+} \)

- Has 1 unpaired electron.

- Spin-only magnetic moment:

$$ \mu = \sqrt{1(1+2)} = \sqrt{3} $$

B. \( Cr^{2+} \)

- Has 4 unpaired electrons.

- Spin-only magnetic moment:

$$ \mu = \sqrt{4(4+2)} = \sqrt{24} $$

C. \( Mn^{2+} \)

- Has 5 unpaired electrons.

- Spin-only magnetic moment:

$$ \mu = \sqrt{5(5+2)} = \sqrt{35} $$

D. \( Fe^{2+} \)

- Has 4 unpaired electrons.

- Spin-only magnetic moment:

$$ \mu = \sqrt{4(4+2)} = \sqrt{24} $$

E. \( Sc^{3+} \)

- Has no unpaired electrons.

- Spin-only magnetic moment:

$$ \mu = 0 $$

Step 3: Compare the Magnetic Moments

• \( Cr^{2+} \) and \( Fe^{2+} \) both have \( \mu = \sqrt{24} \).
• \( Ti^{3+} \) and \( Sc^{3+} \) have different magnetic moments from others.

Step 4: Conclusion

The correct answer is:

Option (1) - B and D only, since they have the same spin-only magnetic moment.