Step 1: Understanding the Concept:
To find the exact number of unpaired electrons in a transition metal ion, we first write the full electron configuration of the neutral atom and then systematically remove electrons to form the specified ion. Electrons are always removed from the outermost shell first (highest principal quantum number $n$).
Step 2: Key Formula or Approach:
Approach: Write the electron configuration for the neutral atom ($\text{Ti}$), remove 3 electrons to form the ion ($\text{Ti}^{3+}$), and apply Hund's rule to the remaining d-electrons.
Step 3: Detailed Explanation:
1. Electron configuration of neutral Titanium ($\text{Ti}$):
The atomic number of $\text{Ti}$ is $22$.
Its ground-state electron configuration is $[\text{Ar}] 3d^2 4s^2$.
2. Electron configuration of $\text{Ti^{+3}$ ion:}
To form a $+3$ ion, the titanium atom must logically lose 3 electrons.
Electrons are lost from the outermost shell ($4s$) first, and only then from the inner shell ($3d$).
- Remove 2 electrons from the $4s$ orbital.
- Remove 1 electron from the $3d$ orbital.
The resulting configuration for $\text{Ti}^{3+}$ is $[\text{Ar}] 3d^1 4s^0$, or simply $[\text{Ar}] 3d^1$.
3. Count unpaired electrons:
The $3d$ subshell has 5 degenerate orbitals. According to Hund's rule, electrons fill degenerate orbitals singly first. The single electron will occupy one of these orbitals unpaired.
Therefore, there is exactly $1$ unpaired electron.
Step 4: Final Answer:
The $\text{Ti}^{+3}$ ion has 1 unpaired electron.