The Physics
Hypertextbook
Opus in profectus

Fission

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Practice

practice problem 1

Write a fission bomb question that could be used in both the fission and nuclear weapons sections.

solution

Answer it.

practice problem 2

Write something about a fission reactor.

solution

Answer it.

practice problem 3

Write something — a fission weapon question that could be reused in the section on nuclear weapons if possible.

solution

Answer it.

practice problem 4

A nucleus is a ball of positively charged protons glued together with the help of uncharged neutrons. Splitting a nucleus into two roughly equal halves increases the overall separation between the protons and reduces their electrostatic potential energy. Determine the fraction of the original electrostatic potential energy released in an idealized fission reaction.

solution

Start with the equation for electrostatic potential energy (Ue) between two point charges.
 
Ue =  kq1q2
r2
 
This will be computed over and over again for every pair of protons in the nucleus. All protons are identical, so…
     
q1 = q2 = e and q1q2 = e2
     
Thus…
 
Uparent = Σ  ke2
r2
 
Dividing a ball of nuclear matter in half results in two spheres with half the charge (e/2) and half the volume (V/2) of the original. Volume is proportional to the cube of radius, so the new spheres will have a diameter that's smaller by the cube root of a half.
   
V ∝ r3  ⇒  V  ∝ 
r 3
2 ∛2
   
Applying these changes to the electrostatic potential energy for one daughter nucleus gives…
 
  Udaughter =  Σ  k(e/2)2  = 
∛2 2
 Σ  ke2  
  (r/∛2)2 2 r2  
  Udaughter =  0.39685… Uparent ≈ 40% Uparent
 
 
Thus, each daughter nucleus has roughly 40% of the electrostatic energy of the parent nucleus. But…

100% ≠ 40% + 40%

The remaining 20% is liberated to do work — like boiling water to make steam to generate electricity or, in the case of nuclear weapons, laying waste to a city.