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In a nuclear reactor, U^(235) undergoes ...

In a nuclear reactor, `U^(235)` undergoes fission libertaing `200 MeV` of energy. The reactor has a `10%` efficiency and produces `1000 MW` power. If the reactor is to function for `10` years, find the total mass of urnaium needed.

Text Solution

Verified by Experts

If m kg is the required mass of the uranium, then number of nuclei
`=((mxx1000)xx6.02xx10^(23))/235`
Each `U_(235)` nucleus releases energy 200 MeV,
`:.` total energy released in 10 years
`E_("in")=(mxx6.02xx10^(26))/235xx200`
Energy required in 10 years `E_("our")=Pt`
`=(1000xx10^(6))xx(10xx365xx24xx360)`
Efficiency `eta=(E_("out"))/(E_("In"))`
Substituting the values we get
`m=3.8xx10^(4)` kg
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