Determine the electronic configuration and number of unpaired electrons for neutral Chromium (Cr) and Cr2+ ion.

Chromium (Cr) has an atomic number of 24, meaning it has 24 electrons. Chromium is an exception to the Aufbau principle, exhibiting a half-filled d-subshell for increased stability.

The electronic configuration for Cr is:

$$\text{Cr: } [\text{Ar}] 3d^5 4s^1$$

The $[Ar]$ core represents 18 paired electrons. We focus on the valence electrons in $3d$ and $4s$ orbitals.
For $4s^1$: one electron in the $4s$ orbital.
For $3d^5$: five electrons, each occupying a separate $3d$ orbital due to Hund's rule.

$$\text{Cr: } \underbrace{\boxed{\uparrow}}_{4s} \quad \underbrace{\boxed{\uparrow}\boxed{\uparrow}\boxed{\uparrow}\boxed{\uparrow}\boxed{\uparrow}}_{3d}$$

Number of unpaired electrons for Cr = $1 (4s) + 5 (3d) = 6$.
The number of unpaired electrons for Cr is $\boxed{\text{6}}$.

Cr$^{2+}$ means the neutral Cr atom has lost 2 electrons. Electrons are removed from the orbital with the highest principal quantum number first. So, the $4s$ electron is removed first, then one $3d$ electron.

Neutral Cr: $[Ar] 3d^5 4s^1$
Remove 1 electron from $4s$: $[Ar] 3d^5 4s^0$
Remove 1 electron from $3d$: $[Ar] 3d^4 4s^0$

The electronic configuration for Cr$^{2+}$ is:

$$\text{Cr}^{2+}\text{: } [\text{Ar}] 3d^4$$

For $3d^4$: four electrons, each occupying a separate $3d$ orbital.

$$\text{Cr}^{2+}\text{: } \underbrace{\boxed{\uparrow}\boxed{\uparrow}\boxed{\uparrow}\boxed{\uparrow}\boxed{\phantom{\uparrow}}}_{3d}$$

Number of unpaired electrons for Cr$^{2+}$ = 4.
The number of unpaired electrons for Cr$^{2+}$ is $\boxed{\text{4}}$.

Cr$^{3+}$ means the neutral Cr atom has lost 3 electrons.
Neutral Cr: $[Ar] 3d^5 4s^1$
Remove 1 electron from $4s$: $[Ar] 3d^5 4s^0$
Remove 2 electrons from $3d$ (to make a total of 3 removed): $[Ar] 3d^3 4s^0$

The electronic configuration for Cr$^{3+}$ is:

$$\text{Cr}^{3+}\text{: } [\text{Ar}] 3d^3$$

For $3d^3$: three electrons, each occupying a separate $3d$ orbital.

$$\text{Cr}^{3+}\text{: } \underbrace{\boxed{\uparrow}\boxed{\uparrow}\boxed{\uparrow}\boxed{\phantom{\uparrow}}\boxed{\phantom{\uparrow}}}_{3d}$$

Number of unpaired electrons for Cr$^{3+}$ = 3.
The number of unpaired electrons for Cr$^{3+}$ is $\boxed{\text{3}}$.