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

How long can an electric lamp of 100W be kept glowing by fusion of 2.0 kg of deuterium? The fusion reaction can be taken as `._1H^2+._1H^2to ._1H^3+n+3.17MeV`

A

`2.4xx10^6` years

B

`7.4xx10^4` years

C

`1.6xx10^6` years

D

`4.9xx10^4` years

Text Solution

Verified by Experts

The correct Answer is:
d
Number of atoms present in 2 g of deuterium `=(6.023xx10^23xx2000)/2=6.023xx10^26`
Energy released in the fusion of 2 deuterium atoms =3.27 MeV
Total energy released in the fusion of 2.0 kg of deuterium atoms
`E=3.27/2xx6.023xx10^26=9.81xx10^26` MeV
`=15.696xx10^13` J
Energy consumed by the bulb per second = 100 J
Time for which the bulb will glow `t=(15.69xx10^13)/100 s` or `t=(15.69xx10^11)/(3.15xx10^7)` years
`=4.9xx10^4` years .
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