Question

Calculate and compare the energy released by (a) Fusion of 1.0 kg of hydrogen deep within Sun (b) The fission of 1.0 kg of ${}^{235}U$ in a fission reactor

Answer 1

A.

Amount of hydrogen, $m=1kg=1000g$

1 mole, i.e.e , 1 g of hydrogen ${(}_1^{1}H)$ contains $6.023\times {10}^{23}$ atoms. Therefore 1000 g of hydrogen contains $6.023\times {10}^{23}\times 1000$ atoms.

Within the Sun, four ${}_1^{1}H$ nuclei combine and form one ${}_2^{4}He$ nucleus. In this process $26MeV$ of energy is released. Hence the energy released from fusion of $1kg$ ${}_1^{1}H$ is

$E_1=\frac{6.023\times {10}^{23}26\times {10}^3}{4}=39.149\times {10}^{26}MeV$

B:

Amount of ${}_{92}^{235}U$= 1 kg = 1000 g

One mole i.e. 235 g of ${}_{92}^{235}U$ contains $6.023\times {10}^{23}$ atoms. Therefore 1000 g of ${}_{92}^{235}U$ contains $\frac{6.023\times {10}^{23}\times 1000}{235}$ atoms.

It is known that the amount of energy released in the fission of one atom of ${}_{92}^{235}$ is $200MeV$

Hence, energy released from the fission of 1 kg of ${}_{92}^{235}$ is

$E_2=\frac{6.023\times {10}^{23}\times 1000\times 200}{235}=5.106\times {10}^{26}MeV$

$\frac{E_1}{E_2}=7.67\approx 8$

Therefore, the energy released in the fusion of 1 kg of hydrogen is nearly 8 times the energy released in the fission of one kg of uranium.