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It is proposed to use the nuclear fusion...

It is proposed to use the nuclear fusion reaction,
`._1^2H+_1^2Hrarr_2^4He`
in a nuclear reactor `200 MW` rating. If the energy from the above reaction is used with a `25` per cent efficiency in the reactor, how many grams of deuterium fuel will be needed per day?(The masses of `._1^2H` and `._2^4He` are `2.0141` atomic mass units and `4.0026` atomic mass units respectively.)

Text Solution

Verified by Experts

Total energy used in nuclear reactor per day
`E=Pt`
`=(200xx10^(6))xx(24xx360)`
`=1.72x10^(12)J`
Energy used in reactor per reaction
`=24/100(2xx2.0141-4.0026)xx931` M eV
`=5.9584MeV`
`=9.5334xx10^(-13)J`
The mass of deuterium used per reaction
`=2xx2.0141=4.0282amu`
`=4.0282/(6.02xx10^(23))g=0.6691xx10^(-23)g`
Thusmass of deuterium required to produce `1.72xx10^(12)` J of energy
`=((0.6691xx10^(-23))xx(1.72xx10^(12)))/(9.5334xx10^(-13))`
`=120g`
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