Question 38 of 44intermediate🔧 ApplyNumerical3 marks

Use Hund's rule to derive the electronic configuration of Ce3+Ce^{3+} ion, and calculate its magnetic moment on the basis of 'spin-only' formula.

Correct Answer

Electronic Configuration of Ce³⁺:

Step 1: Determine atomic number and neutral configuration Cerium (Ce) has atomic number 58. The neutral Ce atom has the electronic configuration: [Xe] 4f¹ 5d¹ 6s².

Step 2: Apply Hund's rule for ion formation According to Hund's rule, electrons are removed from the outermost orbitals first. For Ce³⁺ ion, three electrons are removed in the order: 6s² electrons first, followed by 5d¹ electron.

Step 3: Write the electronic configuration of Ce³⁺ Ce³⁺: [Xe] 4f¹ This configuration has 1 unpaired electron in the 4f orbital.

Calculation of Magnetic Moment:

Step 4: Apply the spin-only formula The spin-only formula for magnetic moment is: μ = √[n(n+2)] BM where n = number of unpaired electrons

Step 5: Substitute the value For Ce³⁺, n = 1 μ = √[1(1+2)] μ = 3\sqrt{3} μ = 1.73 BM

Therefore, the magnetic moment of Ce³⁺ ion is 1.73 Bohr magnetons (BM).

Exercise: EXERCISES | Q: 4.31 | (Page 29)
For More Understanding

Explanation

The question requires deriving Ce³⁺ configuration using Hund's rule. The context confirms that Ce⁴⁺ has noble gas configuration [Xe], which means Ce³⁺ has one additional electron in 4f orbital. The spin-only formula μ = √[n(n+2)] is provided in the context, and the context explicitly states that 'A single unpaired electron has a magnetic moment of 1.73 Bohr magnetons (BM)', confirming the calculation.

Solution Steps

  1. Step 1: Identify Ce atomic number = 58, neutral configuration [Xe] 4f¹ 5d¹ 6s²

  2. Step 2: Remove 3 electrons from outermost orbitals (6s² then 5d¹) to form Ce³⁺

  3. Step 3: Ce³⁺ configuration = [Xe] 4f¹ with 1 unpaired electron

  4. Step 4: Apply spin-only formula μ = √[n(n+2)] where n = 1

  5. Step 5: Calculate μ = 3\sqrt{3} = 1.73 BM

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