Calculating Energy Released in a Fission Reaction: Where Did I Go Wrong?

[songoku]

Homework Statement

Calculate the amount of energy, in joules, generated from 2 kg of uranium fuel, if the U-235 represents 0.7% of the metal and every fission reaction produces 200 MeV.

Relevant Equations

E = mc^2

Energy = $\frac{2000}{235}$ x 6.02 x 10²³ x 0.7% x 200 x 1 x 10⁶ x 1.6 x 10^-19 = 1.15 x 10¹² J

But the answer is 1.15 x 10⁹ J

I am off by a factor of 1000. Where is my mistake?

Thanks

 

[malawi_glenn]

SI units for mass is kg not g

 

[songoku]

SI units for mass is kg not g

Sorry I don't understand the hint.

Wouldn't it be the same if I write: $\frac{2}{0.235}$ instead of $\frac{2000}{235}$?

 

[malawi_glenn]

And I don't understand your solution, it is just a bunch of numbers.

Anyway, do it in steps. First, how many U-235 atoms are there per kg?

 

[songoku]

And I don't understand your solution, it is just a bunch of numbers.

Anyway, do it in steps. First, how many U-235 atoms are there per kg?

Let me redo

1) No. of atoms of U-235 in 2 kg of uranium fuel = $\frac{2000}{235}$ x 6.02 x 10²³ x 0.7% = 3.586 x 10²² atoms

2) Amount of energy released = 200 MeV x No. of atoms = 7.127 x 10²⁴ MeV

3) Convert MeV to Joule = 7.127 x 10²⁴ x 1 x 10⁶ x 1.6 x 10^-19 = 1.15 x 10¹² J

Thanks

 

[malawi_glenn]

And 6.02 x 10²³ is avogadros number, the number of entities in one mol.
U-235 is approx 235g / mol.

Anyway, the answer you quoted is most likely wrong.

 

[songoku]

Thank you very much malawi_glenn