Correct answer: (4) Their metallic properties increase and their atomic radii increase.

Why?:

Atomic radius increase as we go down from top to bottom in the periodic table. This is due to the increase in the number of electrons in an atom. The additional electrons are numerous enough to occupy a new energy level, which determines the size of an atom. Atomic radius decreases as we go across from left to right. Although the number of electrons also increases in the elements from left to right of the periodic table, they occupy the same outermost energy level. No new energy level is created to accommodate them. This means the there are many electrons surrounding the positive nucleus. With this, the attraction between the negative electrons and the positive nucleus gets intensified. This intensified attraction gets the electrons closer to the nucleus. Thus, it makes the atom get smaller in size.

Metallic property decreases as we go from left to right of the periodic table and increases as we go down from top to bottom. This property has something to do with how easily valence electrons can be cleaved off the atom. Elements having 1 to 3 valence electrons are considered metallic because these elements prefer to give up their few valence electrons rather than seek for more to have a complete set of eight valence electrons to be stable. Those having 5 to 7 valence electrons prefer to be added with 1 to 3 more electrons than to give up their valence electrons to have a complete set of 8 valence electrons. These elements are nonmetallic. Fewer valence electrons can be found on the left side of the periodic table. Those with greater number of valence electrons are found on the left side of the periodic table.

Answering this question:

If you cannot analyze how the trend goes or how to come up with a good rationale, it is beneficial to always remember that fluorine is the smallest element and francium is the most metallic element. Locate their positions in the periodic table. It is easy to remember them because they are located in the two corners of the periodic table. Fluorine is the 1^st element under group 17. Knowing this, we would have an idea that the elements below fluorine are bigger.

With francium's location, it can be easily determined that the elements above it are less metallic. You do the same analogy with the elements under group 15.

So this leaves us with (4) as the correct answer.