Step 1: Understanding the Concept:
Magnetic moment ($\mu$) depends on the number of unpaired electrons ($n$). More unpaired electrons mean a higher magnetic moment.
Step 2: Formula Application:
$\mu = \sqrt{n(n+2)} \text{ Bohr Magnetons (BM)}$.
Step 3: Explanation:
1. Cr$^{2+}$ ($d^4$): 4 unpaired electrons.
2. Ni$^{2+}$ ($d^8$): 2 unpaired electrons.
3. Cu$^{2+}$ ($d^9$): 1 unpaired electron.
4. Co$^{3+}$ ($d^6$): 4 unpaired electrons (high spin) or 0 (low spin).
Generally, Cr$^{2+}$ is the most common answer for "highest" in this set as it consistently has 4 unpaired electrons in standard aqueous states.
Step 4: Final Answer:
Cr$^{2+}$ has the highest magnetic moment value.