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NCERT Class XII Chapter
Nuclei
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Question : 19 of 31
Marks: +1, -0
How long can an electric lamp of 100 W be kept glowing by fusion of 2.0 kg of deuterium? Take the fusion reaction as
 12H+ 12H\,\mathrm{}^{2}_{1}\mathrm{H}+\,\mathrm{}^{2}_{1}\mathrm{H} →  23He\,\mathrm{}^{3}_{2}\mathrm{He} + n + 3.27 MeV
Solution:  
Number of atoms present in 2 g of deuterium = 6.023 × 102310^{23}
Total number of atoms present in 2000 g of deuterium
= 6.023×1023×20002\frac{6.023\times10^{23}\times2000}{2} = 6.023 × 102610^{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 = 3.272\frac{3.27}{2} × 6.023 × 102610^{26} = 9.81 × 102610^{26} MeV = 15.696 × 101310^{13} J
Energy consumed by the bulb per second = 100 J
Time for which the bulb will glow
t = 15.69×1013100\frac{15.69\times10^{13}}{100} s or t = 15.69×10113.15×107\frac{15.69\times10^{11}}{3.15\times10^{7}} yearsz = 4.9 × 10410^{4} years
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