Magnesium oxide is an example of A. a basic oxide. B. an acidic oxide. C. a neutral oxide. D. an amphoteric oxide.

Magnesium (Mg) is an alkaline earth metal.

Oxides of metals are generally basic. They react with acids to form salt and water. For example, $MgO + 2HCl \rightarrow MgCl_2 + H_2O$.

Therefore, Magnesium oxide is an example of $\boxed{\text{a basic oxide}}$.

Fractional crystallization is a method used to separate components of a mixture based on differences in their solubility. The substance that is **less soluble** will crystallize out first as the solution cools or the solvent evaporates.

The problem states that $NH_4Cl$ is **more soluble** than $NaCl$. This means $NaCl$ is **less soluble**.

Therefore, when separating the mixture by fractional crystallization, $\boxed{\text{NaCl would crystallize first}}$.

*   **Electron affinity:** Generally decreases from right to left across a period.
*   **Electronegativity:** Generally decreases from right to left across a period.
*   **Atomic radius:** Generally increases from right to left across a period because the number of electron shells remains the same, but the nuclear charge decreases, leading to less attraction on the outermost electrons.
*   **Ionization energy:** Generally decreases from right to left across a period.

Therefore, the periodic property that increases from right to left in the periodic table is $\boxed{\text{Atomic radius}}$.