The Island of Death was on Dulkis. The Dulcians tested nuclear weapons there to see the effects of radiation. The island contained the ruins of a museum displaying Ducian weapons from before their abolition of war.
The Dominators Rago and Toba landed on the island and drained the radiation. They chose it because the crust was thin there and they could easily drill to the core. They planned to cause a planet-wide volcanic eruption that would turn the planet into a power source for their war.
The Second Doctor, Jamie McCrimmon and Zoe Heriot had also arrived upon the island. The Dominators' Quarks captured a group of tourists and they were forced to perform laborious tasks such as carrying the stone that littered the island's ruins.
The Quarks began drilling operations but were attacked by Cully and Jamie. They managed to complete the shaft but the Doctor caught their bomb as it fell. He managed to sneak it on board the Dominator ship, which destroyed it in mid-flight. (TV: The Dominators)