How long can an electric lamp of 100W be kept glowing by fusion of 2.0 kg of deuterium? Take the fusion reactions as `""_(1)^(2)H + ""_(1)^(2)H to ""_(2)^(3)He + n + 3.27 MeV`.

Explanation

Mass of deuterium = `2.0141 xx 2 = 4.0282u = 4.0282 xx 1.66 xx 10^(-27) kg`
No. of fusion in kg of deuterium `= (2)/(4.0282 xx 1.66 xx 10^(-27)) = 2.991 xx 10^(26)kg`
Energy released per fusion = `3.2 MeV = 3.2 xx 10^6 xx 1.6 xx 10^(-19)J`
`:.` Energy released from 2 kg of `""_(1)^(2)H = E = 3.2 xx 10^(6) xx 1.6 xx 10^(-19) xx 2.991 xx 10^(26)J`
`= 1.5314 xx 10^(14)J`
`E = P xx t`
`t = E/P = (1.5314 xx 10^(14))/(100) s = (1.5314 xx 10^(14))/(100 xx 365 xx 24 xx 60 xx 60) = 4.85 xx 10^4` years .