To determine which element in its respective oxidation state does not develop a spin-only magnetic moment, we need to analyze the electronic configurations of the given ions as well as their unpaired electrons. The spin-only magnetic moment arises from unpaired electrons. If an ion has no unpaired electrons, it does not develop a spin-only magnetic moment.

Let's consider each ion one by one:

1. $$\mathrm{Cu}^{2+}$$: The atomic number of copper (Cu) is 29. Its ground-state configuration is:

$$ \mathrm{Cu}: [\mathrm{Ar}] 3d^{10} 4s^1 $$

For $$\mathrm{Cu}^{2+}$$, we remove two electrons, preferably from the outermost shell first (4s) and then from the 3d orbitals:

$$ \mathrm{Cu}^{2+}: [\mathrm{Ar}] 3d^9 $$

The $$\mathrm{Cu}^{2+}$$ ion has 9 electrons in the 3d orbital, with one unpaired electron, thus it exhibits a spin-only magnetic moment.

2. $$\mathrm{Zn}^{2+}$$: The atomic number of zinc (Zn) is 30. Its ground-state configuration is:

$$ \mathrm{Zn}: [\mathrm{Ar}] 3d^{10} 4s^2 $$

For $$\mathrm{Zn}^{2+}$$, we remove two electrons from the outermost shell (4s):

$$ \mathrm{Zn}^{2+}: [\mathrm{Ar}] 3d^{10} $$

The $$\mathrm{Zn}^{2+}$$ ion has a completely filled 3d orbital with no unpaired electrons, meaning it does not exhibit a spin-only magnetic moment.

3. $$\mathrm{Ti}^{3+}$$: The atomic number of titanium (Ti) is 22. Its ground-state configuration is:

$$ \mathrm{Ti}: [\mathrm{Ar}] 3d^2 4s^2 $$

For $$\mathrm{Ti}^{3+}$$, we remove three electrons (two from 4s and one from 3d):

$$ \mathrm{Ti}^{3+}: [\mathrm{Ar}] 3d^1 $$

The $$\mathrm{Ti}^{3+}$$ ion has one unpaired electron in the 3d orbital, thus it exhibits a spin-only magnetic moment.

4. $$\mathrm{V}^{3+}$$: The atomic number of vanadium (V) is 23. Its ground-state configuration is:

$$ \mathrm{V}: [\mathrm{Ar}] 3d^3 4s^2 $$

For $$\mathrm{V}^{3+}$$, we remove three electrons (two from 4s and one from 3d):

$$ \mathrm{V}^{3+}: [\mathrm{Ar}] 3d^2 $$

The $$\mathrm{V}^{3+}$$ ion has two unpaired electrons in the 3d orbital, so it exhibits a spin-only magnetic moment.

From the analysis above, the element with an ion that does not develop a spin-only magnetic moment is:

Option B: $$\mathrm{Zn}^{2+}$$

D And F Block Elements

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