Fission Basics: UNIZOR.COM - Physics4Teens - Atoms - Fission
Channel: Zor Shekhtman on UNIZOR Education
Date: 2023-04-02

UNIZOR.COM - Physics through a Looking Glass of Mathematician
Notes to a video lecture on http://www.unizor.com

Fission

Atoms of certain heavy elements, like uranium-235 or plutonium-239 are not very stable and can split into lighter elements if sufficient external force (like an absorption of a neutron) is applied.
This is called a nuclear fusion.

Below is one of the possible kind of a nuclear fission occurred when a neutron is captured by a nucleus of uranium-235.

This reaction can be described by a nuclear equation
0n1 + 92U235 →
→ 56Ba139 + 36Kr95 + 2·0n1

Indeed, the number of protons on the left side of this equation is 0+92=92, which corresponds to this number on the right side 56+36+2·0=92.
The atomic number (number of protons and neutrons) on the left is 1+235=236, which corresponds to the right side 139+95+2·1=236.

The mass of a nucleus of uranium-235 is 235.043928 atomic mass units (amu).
The mass of a nucleus of barium-139 is 138.908841 amu.
The mass of a nucleus of krypton-95 is 94.939711 amu.
Neutron's mass is 1.007 amu.

The total mass of particles on the left side of equation is
1.007 + 235.043928 ≅
≅ 236.051 amu
The total mass of particles on the right side of equation is
138.908841 + 94.939711 +
+ 2·1.007 ≅ 235.863 amu


Mass Defect & Energy

As we see, in this reaction the resulting mass of fission components is less than the original mass. The difference in mass of 0.188 amu is the mass defect.
Where did this extra 0.188 amu go?
It's converted into energy released during this process of fission.

To calculate the energy that is released by the above process of fission, we use the famous Einstein's formula
E = m·c²
substituting the mass defect of 0.188 amu for mass m in this formula, where
1 amu ≅ 1.66·10−27 kg
and speed of light in vacuum
c≅3·108 m/sec.

The resulting amount of energy EU235 released by the above reaction of fission of a single nucleus of uranium-235 is
EU235 ≅
≅ 0.188·1.66·10−27·9·1016 ≅
≅ 2.809·10−11 J (joules)

An atom of uranium has mass of, approximately, 3.95·10−22 gram.
That means, there are, approximately, 0.253·1022 atoms in 1 gram of uranium.

Let's see how much energy can be released if all nuclei in the 1 gram of uranium-235 split into peaces as described above.
E1gU235 ≅
≅ 2.809·10−11·0.253·1022 ≅
≅ 0.711·1011 J ≅ 20,000 kwh

Burning one gallon of gasoline produces about 4 kilowatt hours of energy.
Therefore, one gram of uranium-235, if all its atoms go through a fission process described above, produce an amount of energy equivalent to about 5,000 gallons of gasoline.



Chain Reaction

The above examples of fission of a single nucleus of uranium-235, when it absorbs a single neutron, show that these reactions can produce more neutrons that one. If these two or three neutrons, in turn, are absorbed by other nuclei, those will split as well, producing more neutrons.

Under certain circumstances this might cause a chain reaction of fission.
These circumstances include, primarily, the amount of uranium-235, its purity and shape.

[See full description is at UNIZOR.COM - Physics 4 Teens - Atoms - Fission]