The code name of the bomb dropped by the U.S. on August 9, 1945, Japanese city Nagasaki was "Fat Man". Plutonium was used in fat man. Hence the correct option is (c).

The fissionable material used in the bombs dropped at Nagasaki (Japan) in 1945 was Plutonium.

Explanation:
Plutonium is a synthetic element that does not occur naturally in significant quantities on Earth. It was first synthesized in a laboratory in 1940 by a team of scientists led by Glenn T. Seaborg. Plutonium-239, the isotope used in the Nagasaki bomb, has a half-life of about 24,100 years.

The development of atomic bombs during World War II involved two different approaches: the uranium-based "Little Boy" bomb and the plutonium-based "Fat Man" bomb. The bomb dropped on Hiroshima on August 6, 1945, was the "Little Boy" bomb, which used uranium-235 as its fissionable material.

However, the bomb dropped on Nagasaki on August 9, 1945, was the "Fat Man" bomb, which used plutonium-239 as its fissionable material. The decision to use plutonium in the Nagasaki bomb was made because uranium-235 was in short supply at the time.

Plutonium-239 is a highly fissionable isotope that can sustain a chain reaction in a nuclear explosion. In the Nagasaki bomb, a subcritical mass of plutonium-239 was brought to a supercritical state by the implosion method. The implosion method involves surrounding the plutonium core with a shell of conventional explosives. When the explosives are detonated, they compress the plutonium core, resulting in a supercritical mass and a rapid release of energy.

The detonation of the "Fat Man" bomb over Nagasaki resulted in a devastating explosion, leveling buildings and causing widespread destruction. It is estimated that approximately 70,000 people were killed instantly, with many more dying later due to injuries and radiation exposure.

In conclusion, the fissionable material used in the bombs dropped at Nagasaki in 1945 was Plutonium-239. The use of this highly fissionable material contributed to the destructive power of the bomb and the devastating impact on the city.