Given,
Power of reactor = 1000 MW = 103 MW
= 109W
= 109 Js-1
Energy generated by reactor in 5 Years = 5 x 365 x 24 x 60 x 60 x 109 J
Average energy generated = 200 MeV
= 200 x 1.6 x 10-13 J
Number of fission taking place or number of U235 nuclei required,
Mass of 6.023 x 1023 nuclei of U = 235 gm = 235 x 10-3 kg
Mass of 8.2125 x 1026 nuclei of U,
Given,
Half life , T = 5.3 years
Strength of radioactive source,
= 8.0 mCi = 8.0 x 10-3 Ci
= 8.0 x 10-3 x 3.7 x 10-10 disintegrations s-1
= 29.6 x 107 disintegrations s-1
Since the strength of the source decreases with time,
But
Number of atoms in 60 g of cobalt = 6.023 x 1023
Therefore,
Mass of 1 atom of cobalt =
Mass of is,
Given,
Average amount of energy released per fission,
Quantity of fissionable material = 1 kg
In 239 gm Pu, number of fissionable atom or nuclei
In 1 g of Pu, number of fissionable atom or nuclei
In 1000 gm of Pu, number of fissionable atom or nuclei,
Therefore,
Total energy released in fission of 25.2 x 1023 Pu nucleus or in fission of 1 kg pure Pu is,
= 180 x 25.2 x 1023
= 4536 x 1023 MeV
= 4.5 x 1026 MeV.
Power of the electric lamp = 100 W
When two nuclei of deuterium fuse together, energy released = 3.2 MeV
Number of deuterium atoms in 2 kg is,
Energy released when nuclei of deuterium fuse together,
If the lamp glows for time t, then the electrical energy consumed by the lamp is 100 t,
100 t =
which is the life span of an electric lamp.
(a) The reaction invoved is,
The difference in mass between the original nucleus and the decay products = 226.02540 u - (222.01750 u + 4.00260 u)
= + 0.0053 u
Energy equivalent or Q-value = 0.0053 x 931.5 MeV
= 4.93695 MeV
= 4.94 MeV
The decay products would emerge with total kinetic energy 4.94 MeV.
Momentum is conserved. If the parent nucleus is at rest, the daughter and the -particle have momenta of equal magnitude p but, in the opposite direction.
Kinetic energy,
Since, p is the same for the two particles therefore the kinetic energy divides inversely as their masses.
The -particle gets of the total i.e.,
(b) The difference in mass between the original nucleus and the decay products = 220.01137 u - (216.00189 u + 4.00260 u)
= 0.00688 u
Q-value or Energy equivalent = 0.00688 x 931.5 MeV
= 6.41 MeV
Energy of the alpha particle,