Ethel and julius rosenberg are most known for which of these events?

Their  conviction for spying for the Soviet Union  

Explanation:

Julius Rosenberg and Ethel Greenglass Rosenberg were American Jews who were executed in 1953 after being denounced and convicted of espionage. The allegations were in connection with the transmission of information about the atomic bomb to the Soviet Union. Their execution was the first of civilians for espionage in United States History.

Since the execution, decoded Soviet telegrams seem to confirm that Julius acted as messenger and recruiter for the Soviets, but doubts about Ethel's involvement in the plot persist. The decision to run the couple was and still is controversial. The other spies captured by the FBI were not executed. Ethel's brother, David Greenglass, who provided documents to Julius, served 10 of his 15-year sentence. Harry Gold, the messenger for Klaus Fuchs, who provided much more detailed information to the Soviets about the atomic bomb, turned 15. Morton Sobell, tried along with the Rosenbergs, turned 17 years and 9 months. In 2008 he admitted that he was a spy and confirmed that Julius was in "a conspiracy that gave the Soviets confidential military and industrial information."