Arrange the following in the increasing order of their spin-only magnetic moment values in free state
(A) $Mn^{3+}$
(B) $Fe^{3+}$
(C) $Sc^{3+}$
(D) $Cr^{3+}$
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (C) (D) (A) (B)
Core Concept:
Spin-only magnetic moment depends on number of unpaired electrons:
μ = √[n(n+2)]
More unpaired electrons → higher magnetic moment
Step 1: Find Electronic Configuration
Sc³⁺ → Sc = 3d¹4s² → Sc³⁺ = 3d⁰ → 0 unpaired
Cr³⁺ → Cr = 3d⁵4s¹ → Cr³⁺ = 3d³ → 3 unpaired
Mn³⁺ → Mn = 3d⁵4s² → Mn³⁺ = 3d⁴ → 4 unpaired
Fe³⁺ → Fe = 3d⁶4s² → Fe³⁺ = 3d⁵ → 5 unpaired
Step 2: Compare Magnetic Moment
More unpaired electrons → higher μ
Sc³⁺ (0) < Cr³⁺ (3) < Mn³⁺ (4) < Fe³⁺ (5)
Option-wise Explanation
Option (C) Sc³⁺
Has no unpaired electrons, so it has the lowest magnetic moment.
Option (D) Cr³⁺
Has three unpaired electrons, giving moderate magnetic moment.
Option (A) Mn³⁺
Has four unpaired electrons, so magnetic moment is higher than Cr³⁺.
Option (B) Fe³⁺
Has five unpaired electrons, giving the highest magnetic moment.
Final Increasing Order:
(C) < (D) < (A) < (B)