After he finished his work, Mendeleev predicted . the properties of sodium, lithium, and potassium
the properties of three undiscovered elements
the atomic numbers of all the known elements
the discovery of the radioactive elements

the properties of three undiscovered elements  is the correct answer.

Explanation:

After he completed his work Mendeleev predicted the properties of the undiscovered elements.

In the year 1871, Dmitri Mendeleev predicted the detailed existence and the properties of the three elements that are undiscovered and he gained tremendous fame.

He left the gap in the table to put the elements which are not identified at that time and by glancing at the physical and chemical properties of an element next to the gap, Mendeleev could predict the properties of the not discovered elements.