Question

In which of the following ions the spin-only magnetic moment is lowest?

• A. \( [Ti(H_2O)_6]^{3+} \)
• B. \( [Mn(H_2O)_6]^{2+} \)
• C. \( [Ni(H_2O)_6]^{2+} \)
• D. \( [Co(H_2O)_6]^{2+} \)
  \bigskip

Hint:

Magnetic moment depends on unpaired electrons. The fewer unpaired electrons, the lower the magnetic moment.

Answer 1

The Correct Option is A

Step 1: Finding the Electronic Configuration
- \( Ti^{3+} \) has an electronic configuration of \( d^1 \) → 1 unpaired electron.
- \( Mn^{2+} \) has \( d^5 \) → 5 unpaired electrons.
- \( Ni^{2+} \) has \( d^8 \) → 2 unpaired electrons.
- \( Co^{2+} \) has \( d^7 \) → 3 unpaired electrons. Step 2: Magnetic Moment Calculation
Magnetic moment (\( \mu \)) is given by: \[ \mu = \sqrt{n(n+2)} \] For \( Ti^{3+} \): \[ \mu = \sqrt{1(1+2)} = \sqrt{3} \approx 1.73 \mu_B \] Since \( Ti^{3+} \) has the lowest unpaired electrons, it has the lowest magnetic moment. \bigskip