Final answer:
The term referring to the geographical dispersion of the Jews in the Persian Empire is the 'diaspora.'
Step-by-step explanation:
Many of the Hebrews did not return to their homeland after the Persian Empire took over and allowed the exiled to go back. Instead, they established communities in other parts of the Persian Empire, initiating a period known as the diaspora. This marked a significant moment in Jewish history where, despite being geographically dispersed, the Jewish people maintained their cultural and religious identity, leading to a widespread presence of Jewish communities across various lands.