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How long an electric lamp of 100 W can b...

How long an electric lamp of 100 W can be kept glowing by fusion of 2.0 kg of deuterium ? The fusion reaction can be taken as `._1^2H + ._1^2H to ._2^3 He + n + 3.2 MeV `

Text Solution

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Number of nucleus in 2 kg of `._1^2H = (6.023xx10^23xx2000)/2=6.023xx10^26`
Energy generated on fusion of these nuclei
`E=(3.2xx6.023xx10^26)/2` MeV
Power of the bulb=100 W
Let the bulb glow for t s.
`therefore` Energy spent =`(100xxt)(1.6xx10^(-13))` MeV
`therefore (100t)/(1.6xx10^(-13)) =(3.2xx6.023)/2xx10^23`
or , `t=(3.2xx6.023xx10^23xx1.6xx10^(-13))/(2xx100)`
`=1.54xx10^12` s
`=4.89xx10^4` y
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