It is proposed to use the nuclear fusion reaction
`_(1)^(2) H +_(1)^(2) H rarr _(2)^(4) He`
in a nucleas of `200MW` rating. If the energy from the above reaction is used with a `25` per cest efficiency in the reactor , how many gram of deuterium fuel will be needed per day (The masses of `_(1)^(2)H and _(4)^(2) He are 2.0141`atomic mass unit and `4.0028`atomic mass unit respectively)

Explanation

`._(1)H^(2)+._(1)H^(2)rarr._(2)H^(4)`
Mass defect: `Deltam = 2xx1.0141 - 4.0026`
`= 0.0256amu`
Equivalent energy `= 0.0256 xx 932.5 = 23.85MeV`
`= 23.85xx1.6xx10^(-13)`
`= 38.15xx10^(-13)J`
Efficient `eta = 25%`
Output energy `= (25)/(100)xx38.15xx10^(-13) = 9.53xx10^(-13) J`
Power output `= (9.53xx10^(-13))/(24xx60xx60) = 1.103xx10^(-17)W`
Number of reactions required is
`(200xx10^(6))/(1.103xx10^(-17)) = 181.32 xx 10^(23)`
Number of `._(1)H^(2)` atoms required `= 2xx181.32 xx 10^(23)`
Mass of deuterium `= m`
`2xx181.32xx10^(23) = (m)/(2)xx6.023xx10^(23)`
`m = 120g`