Final answer:
The atomic bomb program that successfully exploded a nuclear bomb in New Mexico was the Manhattan Project. It was a top-secret research project that employed over 100,000 people and resulted in the detonation of an atomic explosion known as the Trinity Test.
Step-by-step explanation:
The name of the atomic bomb program that successfully exploded a nuclear bomb in New Mexico was the Manhattan Project. It was a top-secret research project launched at the beginning of World War II with the goal of creating a deliverable atomic bomb. The project employed more than 100,000 people in various capacities and successfully detonated an atomic explosion in July 1945, known as the Trinity Test. The following month, two atomic bombs were dropped on the Japanese cities of Hiroshima and Nagasaki.