We need to find the number of 3d-electrons in each of the ions.
Step 1: Electron configuration of neutral atoms.
- Chromium (Cr) has an atomic number of 24, so its electron configuration is:
\[
\text{Cr}: [Ar] \, 3d^5 \, 4s^1
\]
- Copper (Cu) has an atomic number of 29, so its electron configuration is:
\[
\text{Cu}: [Ar] \, 3d^{10} \, 4s^1
\]
- Titanium (Ti) has an atomic number of 22, so its electron configuration is:
\[
\text{Ti}: [Ar] \, 3d^2 \, 4s^2
\]
- Manganese (Mn) has an atomic number of 25, so its electron configuration is:
\[
\text{Mn}: [Ar] \, 3d^5 \, 4s^2
\]
Step 2: Electron configuration of the ions.
- For Cr$^{2+}$: We remove 2 electrons, first from the 4s orbital, then from the 3d orbital. The electron configuration is:
\[
\text{Cr}^{2+}: [Ar] \, 3d^4
\]
Number of 3d-electrons = (4)
- For Cu$^{2+}$: We remove 2 electrons, first from the 4s orbital, then from the 3d orbital. The electron configuration is:
\[
\text{Cu}^{2+}: [Ar] \, 3d^9
\]
Number of 3d-electrons = 9.
- For Ti$^{3+}$: We remove 3 electrons, first from the 4s orbital, then from the 3d orbital. The electron configuration is:
\[
\text{Ti}^{3+}: [Ar] \, 3d^1
\]
Number of 3d-electrons = (1)
- For Mn$^{2+}$: We remove 2 electrons, first from the 4s orbital, then from the 3d orbital. The electron configuration is:
\[
\text{Mn}^{2+}: [Ar] \, 3d^5
\]
Number of 3d-electrons = 5.
Step 3: Arranging in increasing order of 3d-electrons.
- Ti$^{3+}$ has 1 3d-electron.
- Mn$^{2+}$ has 5 3d-electrons.
- Cr$^{2+}$ has 4 3d-electrons.
- Cu$^{2+}$ has 9 3d-electrons.
Thus, the increasing order of 3d-electrons is:
Ti$^{3+}$ (1)<Mn$^{2+}$ (5)<Cr$^{2+}$ (4)<Cu$^{2+}$ (9).
Final Answer:
\[
\boxed{\text{The correct order is (C), (D), (A), (B).}}
\]