In a neutron induced fission of `._92U^235` nucleus, usable energy of `185 MeV` is released. If `._92U^235` reactor is continuously operating it at a power level of `100 MW` power, how long will it take for `1 kg` of uranium to be consumed in this reactor?

Explanation

total number of nucleri in 1 kg of uranium ,
n= (Number of moles)`xx` (Avogadro's number )
`((1000)/(235))(6.02xx10^(23))=2.56xx10^(24)`
by the fission of one nucleus , 185 MeV energy is released . Hence total energy released by the fission of 1 kg of uranium is ,
`E=(2.56xx10^(24))(185xx1.6xx10^(-13))J`
`=7.58xx10^(12)J`
power of the power plant is given 100MW or `10^(8) J//s .`
therefore total time upto which the power plant can be run by 1 kg uranium i s, `t=(7.58xx10^(13))/(10^(8))=7.58xx10^(5)`