All elements in this series are radioactive?

    Actinide series     : All the elements in the actinides series are radiactive

Explanation:

The question is to fill in the blank which series of elements in the periodic table are radiactive.

The answer is the actnide series.

The actinide series is the elements in the same row as actinide since the same actnide (atomic number 89)  to the lawrencium (atomic number 103).

Among other elements, this series include thorium, uranium and plutonium which are very known as radiactive elements, since they are used in nuclear reactors, which use  nuclear fission reactions.

The reason for the radioactivity of these elements is the massive unstable nucleus.

A heavy nucleus means a large amount of positive charge (protons)  concentrated in a tiny region (the nucleus of the atom).

The electrostatic repulsion among those so many protons is not balanced by the strong nuclear force (from the neutrons) resulting in the unstability (radioactivity) of the nucleus.