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 + ₁H² → ₂He³ + n + 3.27 MeV

Sol: ₁H² + ₁H² → ₂He³ + n + 3.27 MeV

No. of atoms in 2 kg of ₁H² is

$\displaystyle = \frac{2}{2}\times 6.023 \times 10^{26} $

= 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.