Name an alkali metal in period 3 and halogen in period 2.

To answer the question, let's first identify the relevant groups of the periodic table.

Alkali Metals
Alkali metals are found in Group 1 of the periodic table. These elements are characterized by having one electron in their outermost shell, which makes them highly reactive.
Period 3 includes the following elements: Sodium (Na), Magnesium (Mg), and Aluminum (Al). The alkali metal in Period 3 is Sodium (Na).
Halogens
Halogens are found in Group 17 (or Group 7A) of the periodic table. These elements have seven electrons in their outermost shell, making them very reactive, especially with alkali metals.
Period 2 includes the following elements: Lithium (Li), Beryllium (Be), Boron (B), Carbon (C), Nitrogen (N), Oxygen (O), Fluorine (F), and Neon (Ne). The halogen in Period 2 is Fluorine (F).
Conclusion
Thus, the answer to the question is:

An alkali metal in Period 3: Sodium (Na)
A halogen in Period 2: Fluorine (F)