Question

Ok so there's fission reaction equation of uranuim-235 to produce krypton-91 and baruim-142.

I think it would look like that: 235/92U +1/0n = 91/36Kr + 142/56Ba + 3 1/0n. Also, I calculated Delta mass = 0.82181076 amu, and Delta Energy=Delta mass * c^2 = 1.226*10^-10 J. (c is speed of light) But I'm not sure in my calculations and I don't know how to use them to answer the following questions:

(a) In 1 kg of uranium-235, there are 2.5612*10^24 atoms. Calculate the energy production per kg of uranuim that undegoes fission.

(b) Liquid gasoline is a mixture of over 100 different hydrocarbons in varying concentrations. The energy density of gasoline is about 46 MJ/kg and is one of the highest for compounds that release energy by breaking chemical bonds. Calculate the ratio of the energy produced in the fission reaction of 1 kg of uranium-235 to that produced in the chemical reaction (combustion) of 1 kg of gasoline. Be sure to comment on the size of the ratio and what it means.

Answer 1

(A) Energy produced per atom (ΔE) = 1.226 X 10^-10 J

Number of atoms in 1Kg of U = 2.5612 X 10²⁴

Hence enrgy released by 1Kg of U = No. of atoms X energy released by one atom

Hence enrgy released by 1Kg of U = 2.5612 X 10²⁴ X 1.226 X 10^-10 J = 3.14 X 10¹⁴J/Kg

1MJ = 10⁶J

Hence 3.14 X 10¹⁴J/Kg = 3.14 X 10⁸ MJ/Kg

(B) Energy ratio = Energy released by 1KgU-235 / Energy released by 1Kg gasoline

Energy Ratio = 3.14 X 10⁸ MJ/Kg / 46 MJ/Kg = 6.83 X 10⁶ =

It means energy released by fixed amount of U-235 is 6.83 X 10⁶ times more than energy released by same amount of gasoline