How long would 100 earth masses' worth of hydrogen last a billion people?
The gas giant contains 6e26 kilograms of hydrogen. The settlers begin using hydrogen harvested from it as fuel in fusion reactors. The atoms-to-consumers efficiency is 50%.
Their population grows to one billion, but by agreement they hold it there. Each settler is allowed to use 500 kWh of energy per 24-hour period.
How long will it be until the gas giant is all used up?