Hydrogen bomb

The hydrogen bomb or "H-Bomb" was a type of nuclear weapon produced on Earth during the 20th century. Hydrogen bombs utilized the principle of nuclear fusion instead of nuclear fission.

According to Captain James T. Kirk, the H-bomb was the ultimate weapon of the 20th century, and was described as a "doomsday machine": a weapon primarily built for bluff, never intended for actual use. The USSR (aka the Reds) tested its first H-bomb in 1953, which made headlines in US newspapers. 

In 1968, as part of the nuclear arms race, an orbital H-bomb was launched by NASA, in the US, to counter a similar move by other powers on Earth. The sabotage and subsequent detonation of this suborbital warhead eventually led to a stronger international agreement to ban such orbital weapons. 

In 2267, the overload of the impulse engines of the USS Constellation (NCC-1017) resulted in a fusion explosion of 97.835 megatons. The detonation was used to destroy the Planet killer. Kirk noted the similarity between the overload to that of an H-bomb detonation. He also noted that it was propably the first constructive use of such a weapon. 

Background
It's possible the fusion bombs used by Vendikar and Eminiar VII in were a type of hydrogen bomb.

In a scene scripted, but not included in the final airing of, the sabotage of the gateway complex on Iconia was said to have resulted in a detonation equivalent to a level 12 hydrogen explosion with a blast radius of 900 kilometers. In the final scene of the episode the explosion was seen from orbit.

In The Making of Star Trek, the H-bomb was used as a comparison for the energy produced by a warp core. The difference between the two is comparable to the difference between lighting a match and nuclear energy. (page 192)

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Nuklearwaffe Bombe H