Answer:
\[t=4.9\times {{10}^{4}}\] years According to the concept of Avogadro number, the number of atoms in 2g of \[_{1}^{2}H=6.023\times {{10}^{23}}\] \[\therefore \] The number of atoms in 2 kg of \[_{1}^{2}H\] \[=\frac{6.023\times {{10}^{23}}}{2}\times 2000\] \[=6.023\times {{10}^{26}}\,\,\text{atoms}\] The energy released in fusion of 2 atoms = 32 MeV \[\therefore \] Total energy released in fusion of 2 kg of deuterium \[=\frac{6.023\times {{10}^{23}}}{2}\times 3.2\,\,\text{MeV}\] \[=3.0115\times {{10}^{26}}\times 32\times 1.6\times {{10}^{-19}}\times {{10}^{6}}\,\,\text{J}\] \[=15.42\times {{10}^{13}}\,\,\text{J}\] Power rating of the electric lamp \[=100\,\,\text{W}\] Energy = Power \[\times \] time \[\therefore \] Time for which the lamp glows \[=\frac{\text{Energy}}{\text{Power}}\] \[=\frac{15.42\times {{10}^{13}}}{100}\] \[=15.42\times {{10}^{11}}\,\,\text{seconds}\] \[=4.9\times {{10}^{4}}\,\,\text{years}\]
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