To determine the number of unpaired electrons in the gaseous ions Mn³⁺, Cr³⁺, V³⁺, and Ti³⁺, follow these steps:

Step 1: Write the Electronic Configurations of Neutral Atoms

Using atomic numbers:

• Mn (Z = 25): [Ar] 3d⁵ 4s²
• Cr (Z = 24): [Ar] 3d⁵ 4s¹ (due to half-filled stability)
• V (Z = 23): [Ar] 3d³ 4s²
• Ti (Z = 22): [Ar] 3d² 4s²

Step 2: Remove Electrons for the Given Ion

Since these are +3 ions, remove three electrons starting from the 4s orbital first (lower energy than 3d):

1. Mn³⁺: Remove 3 electrons from Mn (4s², then 3d¹)
   • Mn³⁺: [Ar] 3d⁴
2. Cr³⁺: Remove 3 electrons from Cr (4s¹, then 3d²)
   • Cr³⁺: [Ar] 3d³
3. V³⁺: Remove 3 electrons from V (4s², then 3d¹)
   • V³⁺: [Ar] 3d²
4. Ti³⁺: Remove 3 electrons from Ti (4s², then 3d¹)
   • Ti³⁺: [Ar] 3d¹

Step 3: Count the Number of Unpaired Electrons

The number of unpaired electrons depends on the 3d subshell filling:

Final Answer:

The number of unpaired electrons in:

• Mn³⁺ = 4
• Cr³⁺ = 3
• V³⁺ = 2
• Ti³⁺ = 1