Fission Energy Vs. Total Energy of Uranium-235

The fission of one atom of uranium-235 releases 3.24 × 10^-11 Joules of energy. One mole of atoms (235 grams) produces 6.022 x 10²³ times that amount of energy.¹ How much energy is that?

Energy From Splitting One Mole Uranium-235 Atoms

We calculate,

E_{one mole} ²³⁵U = 3.24 x 10^-11 x 6.022 x 10²³ = 1.95 x 10¹³ Joules or 19,500,000,000,000 Joules.

This is a tremendous amount of energy. It is the energy of each mole of uranium found in an atomic bomb! It is millions of times more energy than any chemical reaction.

But is this the ultimate energy matter can produce? By no means!

Total Energy in One U-235 Atom

When an atom of uranium is split, it does not entirely disappear. Rather, fragments are produced – atoms of other elements. In our scenario, krypton and barium, plus neutrons, replace uranium. The energy released is by no means the entire amount of energy in the atom.

One atom of ²³⁵U has a mass of,

235 grams / 6.022 x 10²³ = 3.90 x 10^-22 grams

Consuming that one atom produces how much energy? Using Einstein’s first order approximation, E=mc², we calculate,

E = [3.90 x 10^-22 grams][1 kilogram/1000 grams][299.8 x 10⁶ meters/second]²

or,

3.51 x 10^-8 Joules

Comparison of One Atom of Each

Thus, we have,

Fission of one ²³⁵U atom: 3.24 x 10^-11 Joules
Total Energy in one ²³⁵U atom: 3.51 x 10^-8 Joules

So our uranium atom contains more than 1,000 times the energy produced by merely splitting the atom.

¹ One mole equals one molecular weight (or in this instance, an atomic weight) in grams of a substance. One mole of ²³⁵U = 235 grams. It consists of 6.022 x 10²³ atoms.

Note: You might also enjoy Do Lone Atoms or Molecules Assume States of Matter?

References:

• Atomic Archive: Nuclear Fission: Basics

← Back to QS Nuggets
← Home