Spin-only magnetic moment: Class 12 practice
μ = √(n(n + 2)) BM, where n is the number of unpaired d electrons. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Electronic configuration
The idea behind spin-only magnetic moment
μ = √(n(n + 2)) BM, where n is the number of unpaired d electrons. Find the ion's d-electron count (group number minus charge for the 3d series), then fill orbitals by Hund's rule.
Step-by-step method
- Write the d-electron count of the ion.
- Place electrons singly first (Hund's rule), count unpaired.
- μ = √(n(n + 2)).
Worked example 1 (Basic)
Find the spin-only magnetic moment of Co²⁺.
- d-electrons: 7
- Unpaired: 3
- μ = √(3 × 5) = 3.87 BM
- Answer: 3.87 BM
Worked example 2 (Standard)
Find the spin-only magnetic moment of Sc³⁺.
- d-electrons: 0
- Unpaired: 0
- μ = √(0 × 2) = 0 BM
- Answer: 0 BM
Worked example 3 (Challenge)
Find the spin-only magnetic moment of Fe²⁺.
- d-electrons: 6
- Unpaired: 4
- μ = √(4 × 6) = 4.9 BM
- Answer: 4.9 BM
Common mistakes and misconceptions
- Removing 3d electrons before 4s
- Counting paired electrons
Practice questions
- (Basic) Find the spin-only magnetic moment of Cr³⁺.
- (Basic) Find the spin-only magnetic moment of Mn²⁺.
- (Standard) Find the spin-only magnetic moment of Ti³⁺.
- (Standard) Find the spin-only magnetic moment of Zn²⁺.
- (Challenge) Find the spin-only magnetic moment of Fe³⁺.
- (Challenge) Find the spin-only magnetic moment of Cr²⁺.
Answer key with full working
- Q1: d-electrons: 3 → Unpaired: 3 → μ = √(3 × 5) = 3.87 BM → Answer: 3.87 BM
- Q2: d-electrons: 5 → Unpaired: 5 → μ = √(5 × 7) = 5.92 BM → Answer: 5.92 BM
- Q3: d-electrons: 1 → Unpaired: 1 → μ = √(1 × 3) = 1.73 BM → Answer: 1.73 BM
- Q4: d-electrons: 10 → Unpaired: 0 → μ = √(0 × 2) = 0 BM → Answer: 0 BM
- Q5: d-electrons: 5 → Unpaired: 5 → μ = √(5 × 7) = 5.92 BM → Answer: 5.92 BM
- Q6: d-electrons: 4 → Unpaired: 4 → μ = √(4 × 6) = 4.9 BM → Answer: 4.9 BM
Syllabus note
This skill is listed under "d and f Block Elements" for Class 12 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is spin-only magnetic moment in?
"d and f Block Elements", Class 12 Chemistry (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.