Nuclear fission

Energy Transfer and Radiation

• Fission is driven by energy transferring out of the nuclear potential energy store of the parent nucleus.
• This energy is transferred to the kinetic energy stores of the newly formed daughter nuclei and the emitted neutrons, causing them to move at extremely high speeds.
• Additional energy is released as electromagnetic radiation in the form of gamma rays, which carry away excess energy as the new nuclei settle into a stable state. Gamma rays have no mass or charge, so they do not affect equation balancing.
• The fundamental reason for this massive energy release is mass-energy equivalence ($E=mc^2$). The total mass of the products is slightly less than the mass of the original nucleus and neutron; this "missing mass" is converted into energy.
• As the fast-moving daughter nuclei and neutrons collide with surrounding materials in a reactor, they transfer energy, increasing the thermal energy store of the surroundings to generate electricity.

Worked Example: Balancing a Fission Equation

Determine the number of neutrons ($x$) released in the following balanced nuclear equation for the fission of Uranium-235:

$_{0}^{1}\text{n} + _{92}^{235}\text{U} \rightarrow _{56}^{141}\text{Ba} + _{36}^{92}\text{Kr} + x _{0}^{1}\text{n} + \gamma$

Step 1: Calculate the total mass number (top numbers) on the left-hand side (LHS) of the equation.

• $\text{LHS Mass Number} = 1 + 235 = 236$

Step 2: Calculate the total mass number of the known fragments on the right-hand side (RHS).

• $\text{RHS Known Mass} = 141 + 92 = 233$

Step 3: Use the conservation rule to find the missing mass.

• $\text{Missing Mass} = 236 - 233 = 3$

Step 4: Determine the number of neutrons ($x$).

• Since each neutron has a mass number of $1$, there must be $3$ neutrons produced to balance the equation.
• $x = 3$

Chain Reactions and Reactor Control

• The two or three high-speed neutrons released during a single fission event act as triggers for further reactions.
• If these neutrons are absorbed by other nearby large, unstable nuclei, they cause those nuclei to split, releasing even more neutrons in a self-sustaining cycle called a chain reaction.
• Critical mass is the minimum amount of fissionable material needed to maintain a self-sustaining chain reaction. If the mass is below this, too many neutrons escape before triggering further fission.
• If a chain reaction is left uncontrolled, the number of fission events increases exponentially, releasing a massive amount of energy in a fraction of a second (the principle behind a nuclear weapon).
• To generate steady power, nuclear reactors maintain a controlled chain reaction, ensuring that, on average, only one neutron from each fission event triggers a subsequent fission.
• Control rods (made of materials like boron) are lowered into the reactor to absorb excess neutrons and limit the rate of the reaction.
• The reactor also contains a moderator (like water or graphite) which slows down the fast-moving neutrons so they can be successfully absorbed by the uranium fuel nuclei.