Question

Which of the following pairs of ions will have same spin only magnetic moment values within the pair?
A. Zn²⁺, Ti²⁺
B. Cr²⁺, Fe²⁺
C. Ti³⁺, Cu²⁺
D. V²⁺, Cu⁺
Choose the correct answer from the options given below:

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

Answer 1

The Correct Option is D

To determine which pairs of ions have the same spin-only magnetic moment values, let's calculate the spin-only magnetic moment for each ion using the formula:

\(\mu = \sqrt{n(n+2)}\) 

where \(n\) is the number of unpaired electrons.

1. For Zn²⁺:
   • Electronic configuration of Zn: [Ar] 3d¹⁰ 4s²
   • Zn²⁺: [Ar] 3d¹⁰
   • Unpaired electrons: 0
   • Spin-only magnetic moment, \(\mu = 0\)
2. For Ti²⁺:
   • Electronic configuration of Ti: [Ar] 3d² 4s²
   • Ti²⁺: [Ar] 3d²
   • Unpaired electrons: 2
   • Spin-only magnetic moment, \(\mu = \sqrt{2(2+2)} = 2.83 \, \text{BM}\)
3. For Cr²⁺:
   • Electronic configuration of Cr: [Ar] 3d⁵ 4s¹
   • Cr²⁺: [Ar] 3d⁴
   • Unpaired electrons: 4
   • Spin-only magnetic moment, \(\mu = \sqrt{4(4+2)} = 4.90 \, \text{BM}\)
4. For Fe²⁺:
   • Electronic configuration of Fe: [Ar] 3d⁶ 4s²
   • Fe²⁺: [Ar] 3d⁶
   • Unpaired electrons: 4
   • Spin-only magnetic moment, \(\mu = \sqrt{4(4+2)} = 4.90 \, \text{BM}\)
5. For Ti³⁺:
   • Electronic configuration of Ti: [Ar] 3d² 4s²
   • Ti³⁺: [Ar] 3d¹
   • Unpaired electrons: 1
   • Spin-only magnetic moment, \(\mu = \sqrt{1(1+2)} = 1.73 \, \text{BM}\)
6. For Cu²⁺:
   • Electronic configuration of Cu: [Ar] 3d¹⁰ 4s¹
   • Cu²⁺: [Ar] 3d⁹
   • Unpaired electrons: 1
   • Spin-only magnetic moment, \(\mu = \sqrt{1(1+2)} = 1.73 \, \text{BM}\)
7. For V²⁺:
   • Electronic configuration of V: [Ar] 3d³ 4s²
   • V²⁺: [Ar] 3d³
   • Unpaired electrons: 3
   • Spin-only magnetic moment, \(\mu = \sqrt{3(3+2)} = 3.87 \, \text{BM}\)
8. For Cu⁺:
   • Electronic configuration of Cu: [Ar] 3d¹⁰ 4s¹
   • Cu⁺: [Ar] 3d¹⁰
   • Unpaired electrons: 0
   • Spin-only magnetic moment, \(\mu = 0\)

Now, comparing the calculated values to find ions with the same spin-only magnetic moment:

• Cr²⁺ and Fe²⁺ both have \(\mu = 4.90 \, \text{BM}\).
• Ti³⁺ and Cu²⁺ both have \(\mu = 1.73 \, \text{BM}\).

Thus, the correct answer is B and C only.