What was a prime motivation for russia's colonial expansion in the late nineteenth and early twentieth centuries?

access to warm-water ports.

Explanation:

A warm-water port is a port where the water does not freeze in winter since they are available yearly.they are used to improve the geopolitical or economic interest and due to this  Russia needed a warm water port to have a well-rounded economy like China or America.

radioactive dating, also known as  radioisotope dating  is a process that in  estimating the approximate  age  of  rocks. these data can be analyzed from  the studies dealing with the  decay of the radioactive elements that are present in these rocks. in nature, there are a few types of materials or atoms which are quite unstable and they spontaneously decay or breakdown to form other kinds of atoms.