Question

Calculate and compare the energy released by a) fusion of 1.0 kg ofhydrogen deep within Sun and b) the fission of 1.0 kg of 235U in afission reactor.

Answer 1

a)

Given: The amount of hydrogen is 1 kg.

Since, 1 g of hydrogen contains 6.023× 10 23  atoms So, 1000 gof hydrogen contains 6.023× 10 23 ×1000 atoms and the fusion of hydrogen deep within the sun has four hydrogen nuclei combining to form one helium nucleus so in this whole process 26 MeVof energy is released.

The energy released from the fusion of 1 kg H 1 1 is given as,

E= n× E ″ N

Where, the numbers of atoms are n, the released energy is E ″ and the numbers of combined atoms are N.

By substituting the given values in the above formula, we get

E= 6.023× 10 23 ×1000×26 4 =39.1495× 10 26  MeV

Thus, the energy released from the fusion of 1 kg H 1 1 is 39.1495× 10 26  MeV.

b)

Given: The amount of U 92 235 is 1 kg.

Since, 235 g of U 92 235 contains 6.023× 10 23  atoms So, 1000 gof hydrogen contains 6.023× 10 23 ×1000 235  atoms and the amount of energy released in the fission of one atom of U 92 235 is 200 MeV.

The energy released from the fusion of 1 kg U 92 235 is given as,

E 1 = n× E ′ N

Where, the numbers of atoms are n, the released energy is E ′ and the numbers of combined nuclei are N.

By substituting the given values in the above formula, we get

E 1 = 6.023× 10 23 ×26×1000 235 =5.106× 10 26  MeV

The ratios of released energies is given as,

E E 1 = 39.1495× 10 26 5.106× 10 26 =7.67 ≈8

Thus, the energy released from the fusion of 1 kg U 92 235 is 5.106× 10 26  MeV and the energy released in the fusion 1 kg of hydrogen is approximately 8times the energy released in fission 1 kgof U 92 235 .