Question

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`

Answer 1

`._(1)H^(2) + ._(1)H^(2) rarr ._(2)^(3) He+n+3.27 MeV`
No. of atoms in `2 kg` of `._(1)H^(2)=2//2xx6.023xx10^(26)=6.023xx10^(26)` atoms
In the above reaction two deuterium nuclei are combined
Power `(p)= w x` rate of fussion.
`=3.27MeV xx ("Number of atoms")/("Time expended")`
`100=3.27xx10^(6)xx1.6xx10^(-19)x(6.023xx10^(26))/(2x)`
`:. x=(3.27xx1.6xx6.023xx10^(+11))/(2)=15.756xx10^(11)S`
`=(15.756xx10^(11))/(365xx24xx60xx60)=(15.756xx10^(11))/(3.15xx10^(7))`
`=5xx10^(4)` years