What city was the capital of the eastern half of what happened to the western half of the Roman Empire

"Constantinople" was the capital of the eastern half of the Roman empire

Explanation:

With the division of Rome, Constantinople became the capital city of the Eastern Roman Empire, while Rome remained as capital of the Western half of the Roman Empire. Emperor Theodosius I distributed both halves between his sons Honorius (in charge of the west part of the divided empire) and Arcadius (Emperor of the eastern side). The first one was highly affected by invasions of goths and barbarians from the north side, debilitating the roman military force as well as the culture of the Empire.