Introduction:
The spin-only magnetic moment is a measure of the magnetic behavior of a compound or ion. It is calculated using the formula:

μs = √(n(n+2))

Where μs is the spin-only magnetic moment in Bohr magneton units, and n is the number of unpaired electrons.

Cr(CO)6:
Cr(CO)6 is a coordination complex consisting of a central chromium (Cr) atom bonded to six carbon monoxide (CO) ligands. To determine the spin-only magnetic moment of Cr(CO)6, we need to determine the number of unpaired electrons.

Electronic Configuration of Chromium:
The atomic number of chromium is 24, and its electronic configuration is [Ar] 3d^5 4s^1. In the case of Cr(CO)6, the chromium ion loses one electron to form a Cr(0) complex.

Determining the Number of Unpaired Electrons:
To determine the number of unpaired electrons, we need to consider the electronic configuration of the Cr(0) ion. Since chromium has a d^5 configuration, it is expected to have 5 unpaired electrons. However, the presence of ligands can cause electron pairing or splitting of the d orbitals.

Ligand Field Theory:
According to Ligand Field Theory, the carbon monoxide (CO) ligands act as strong field ligands, causing the d orbitals to split into two sets: t2g (lower energy) and eg (higher energy).

Electron Configuration in the Ligand Field:
In the presence of strong field ligands, the electrons prefer to occupy the lower energy t2g orbitals. Therefore, the 5 d electrons of the Cr(0) ion will occupy the t2g orbitals in a paired manner, resulting in zero unpaired electrons.

Calculating the Spin-Only Magnetic Moment:
Using the formula μs = √(n(n+2)), where n is the number of unpaired electrons, we find that for Cr(CO)6, n = 0. Plugging this value into the formula, we get:

μs = √(0(0+2)) = √(0) = 0

Therefore, the spin-only magnetic moment of Cr(CO)6 is zero Bohr magneton units.

Conclusion:
The spin-only magnetic moment of Cr(CO)6 is zero because all the d electrons of the Cr(0) ion are paired up in the presence of strong field ligands.