JEE Main · 2024 · Shift-IImediumDNF-002

A first row transition metal in its +2 oxidation state has a spin-only magnetic moment value of 3.86 BM. The atomic…

d & f-Block Elements · Class 12 · JEE Main Previous Year Question

Question

A first row transition metal in its +2 oxidation state has a spin-only magnetic moment value of 3.86 BM. The atomic number of the metal is:

Options
  1. a

    26

  2. b

    25

  3. c

    23

    ✓
  4. d

    22

Correct Answerc

23

Detailed Solution

Spin-only magnetic moment: μ=n(n+2)\mu = \sqrt{n(n+2)} BM

Given μ=3.86\mu = 3.86 BM: n(n+2)≈14.9⇒n=3(15=3.87 BM)n(n+2) \approx 14.9 \Rightarrow n = 3 \quad (\sqrt{15} = 3.87 \text{ BM})

Need ion with 3 unpaired electrons in +2 state:

| Z | M²⁺ Config | Unpaired e⁻ | |---|------------|-------------| | 26 (Fe) | 3d63d^6 | 4 | | 25 (Mn) | 3d53d^5 | 5 | | 23 (V) | 3d33d^3 | 3 ✓ | | 22 (Ti) | 3d23d^2 | 2 |

V2+\text{V}^{2+}: 3d33d^3 → 3 unpaired electrons → μ=15=3.87\mu = \sqrt{15} = 3.87 BM ✓

Answer: Option (3) — Z = 23 (Vanadium)

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