Question

In the sun, 1000g of hydrogen fuses to 993g of helium while the other 7g of matter is converted into energy using Einstein's famous equation E=mc2, where c is the speed of light (3.0*108m/s).

1. What is the ratio of the energy released by the fusion of 1.0 kg of hydrogen to that released by fission of 1.0 kg of Uranium-235?

2. Given the obvious advantage in energy production, briefly describe some of the difficulties in designing and operating a fusion power plant to explain why there are no commercial fusion power plants in operation today.

Answer 1

In fission of 1 atom of Uranium-235

3.102x10^-28 kg mass converted into energy:

Einstein's equation ;E = mc^2

E = (3.102x10^-28 Kg/atom)(3.00x10^8 m/s)^2

= 2.79x10^-12 J/atom

Now convert J/atom to kJ/mol:

(2.79x10^-12 J/atom) x [(6.022x10^23 atoms)/(1 mole)] x [(1 kJ)/(1000 J)] = 1.68x10^8 kJ/mol

Here the total mass of U -235= 1000 g , ,means number of moels = 1000 g/ 235 g/mol=4.26 mol

Now calculate the total energy= 1.68x10^8 kJ/mol *4.26 mol

= 7.2*10^8 KJ.

Now given that; In the sun, 1000g of hydrogen fuses to 993g of helium while the other 7g of matter is converted into energy.

7.0 g = 0.007 kg

Einstein's equation ;E = mc^2

E = (0.007 Kg)(3.00x10^8 m/s)^2

= 6.3*10^14 J
=6.3*10^11 KJ

Now calculate the ratio of the energy released by the fusion of 1.0 kg of hydrogen to that released by fission of 1.0 kg of Uranium-235:

6.3*10^11 KJ/ 7.2*10^8 KJ. = 875 :1

The energy released by the fusion of 1.0 kg of hydrogen : released by fission of 1.0 kg of Uranium-235: