How long can be electric lamp of 100 W be kept glowing by fusion of 2.0 kg of deuterium ? take the fusion reaction as…

Q: How long can be electric lamp of 100 W be kept glowing by fusion of 2.0 kg of deuterium ? take the
fusion reaction as 1H2 + 1H22He3 + n + 3.27 MeV

Sol: 1H2 + 1H22He3 + n + 3.27 MeV

No. of atoms in 2 kg of 1H2 = 2/2 x 6.023 x 1026

= 6.023 x 1026 atoms.

In the above reaction two deuterium nuclei are combined power (P) = W × rate of fusion.

= 3.2 MeV × (Number of atoms)/(Time exp⁡ended )

100 = 3.27 x 106 x 1.6 x 10-19 x (6.023 × 1026)/2x

x = (3.27 × 1.6 × 6.023 × 1011)/2 = 15.756 x 1011 S

= (15.756 × 1011)/(365 × 24 × 60 × 60)

= (15.756 × 1011)/(3.15 × 107 ) = 5 x 104 years.