What is the power output of a `._(92) U^(235)` reactor if it is takes `30` days to use up `2 kg` of fuel, and if each fission gives `185 MeV` of usable energy ?.

Explanation

Here, `t=30days=30xx24xx60xx60s`
`m=2kg`
Energy `//` fission `=85MeV=185xx1.6xx10^(-13J`
`N=6xx10^(23)//mol e`
Mass of fuel consumed `//` sec
`m=(2)/(30xx24xx60xx60)kg`
`=(2xx1000)/(3xx24xx36xx1000)gram`
`=(1)/(36xx36)gram`
Now, number of atoms in 235 g of `_(92)U^(235)`
`=6xx10^(23)`
`:.` Number of atoms which undergo fission per second `=(6xx10^(23))/(235)xx(1)/(36xx36) :.` Energy released `//` sec
`=(6xx10^(23))/(235xx36xx36)xx185xx1.6xx10^(-13)"watt"`
i.e., Power output `=(6xx185xx1.6)/(235xx36xx36)xx10^(10 )"watt"`
`=5.83xx10^(7)wat t`
`=58.3 MW`