Nuclear Energy: Fission & Nuclear Reactor

Table of Contents
1. Nuclear Fission
2. Nuclear Chain Reaction
3. Nuclear Reactor
4. Nuclear Fusion
5. Thermonuclear Energy
6. Fission vs Fusion
7. Solved Examples
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Nuclear Fission

Nuclear fission is the process in which a heavy nucleus splits into two or more lighter nuclei, accompanied by the release of neutrons and a large amount of energy.

An important example is the fission of ₉₂U²³⁵ induced by a slow (thermal) neutron:

Energy released per fission ≈ 200 MeV = 3.2 × 10⁻¹¹ J. This energy arises from the mass defect between the initial nucleus plus incident neutron and the final products; the difference appears as kinetic energy of the fragments and the emitted neutrons, and as gamma radiation. The quantitative energy (Q-value) of a nuclear reaction is given by the mass difference multiplied by c²:
                                                                                                                        Q = (Initial mass  - final mass) c²
                                                                                                                                                      OR

Key numbers to remember:

• Energy per fission of U-235 ≈ 200 MeV
• 1 kg of U-235 contains ≈ 2.56 × 10²⁴ atoms
• Total energy from 1 kg U-235 ≈ 8.2 × 10¹³ J

Nuclear Chain Reaction

Nuclear chain reaction occurs when one fission event produces neutrons that go on to induce further fissions, thereby sustaining a sequence (chain) of reactions.

Key points and terminology:

• Multiplication factor (k): the average number of neutrons from one fission that cause another fission.
  • k < 1 : subcritical (chain dies out)
  • k = 1 : critical (steady chain reaction - used in reactors)
  • k > 1 : supercritical (reaction grows exponentially - basis of nuclear explosives)
• Critical mass: the minimum amount of fissile material required to sustain a chain reaction under given conditions (geometry, moderator, reflectors, etc.).

Chain reactions may be of two types:

• Controlled chain reaction - the rate of fission is regulated (for example, in a nuclear reactor) so that k is maintained about unity and energy release is steady and usable.
• Uncontrolled chain reaction - the fission rate increases rapidly (k > 1) leading to an explosive release of energy (principle of an atomic bomb).

Nuclear Reactor

A nuclear reactor is an engineered device in which a controlled nuclear chain reaction is maintained to produce heat for electricity generation or for other purposes (research, propulsion, isotope production).

The main parts and their functions:

• Fuel - fissile or fertile materials placed in fuel rods. Common materials include ₉₂U²³⁵ (fissile) and Pu²³⁹ (fissile). ₉₂U²³⁸ is fertile: it can capture neutrons and convert to Pu-239, which is fissile.
• Moderator - a material that slows down fast neutrons to thermal energies so that they are more likely to induce fission in fissile nuclei. Typical moderators are heavy water (D₂O), graphite, and beryllium oxide.
• Coolant - a fluid that removes heat from the reactor core and transfers it to a steam generator or directly to turbines. Common coolants include ordinary water, heavy water, liquid sodium, and gases such as CO₂ or helium.
• Control rods - rods made of materials with a high neutron-absorption cross-section (for example, cadmium, boron, or hafnium). Inserting or withdrawing control rods changes the neutron population and controls the fission rate.
• Shielding and containment - concrete, lead, steel and other structures protect personnel and the environment from ionising radiation; a containment building prevents release of radioactive material in accidents.
• Reactor core - the region containing fuel assemblies, moderator and coolant where fission reactions occur.

In power reactors the heat produced by fission is used to generate steam that drives turbines; precise control and heat removal are essential for safety. An atom bomb works on the principle of an uncontrolled chain reaction, where fissile material is rapidly brought to a supercritical configuration.

Nuclear Fusion

Nuclear fusion is the process in which two light nuclei combine to form a heavier nucleus, with a net release of energy when the binding energy per nucleon of the product is greater than that of the reactants.

Common fusion reactions of interest:

• Deuterium-tritium (D-T) fusion: ₁H² + ₁H³ → ₂He⁴ + ₀n¹ + 17.6 MeV
• Deuterium-deuterium (D-D) reactions: D + D → He^-3 + n (3.27 MeV) or D + D → T + p (4.03 MeV)

Some textbook presentations give a simplified net reaction in which three deuterons combine to form an alpha particle (₂He⁴) with an overall release of energy (a commonly quoted value is ~21.6 MeV for a particular net process). Actual fusion proceeds via intermediary steps (D-D and D-T channels) as shown above.

Fusion releases very large amounts of energy per unit mass of fuel compared with chemical reactions.

Conditions Required for Fusion
Nuclear fusion requires extremely high temperatures and pressures to overcome the Coulomb repulsion between positively charged nuclei:

• Temperature required ≈ 10⁷ K or more
• At such temperatures, matter exists as plasma (fully ionized gas)
• This state is called thermonuclear condition
• Sun achieves fusion through its enormous gravitational pressure and core temperature of ~1.5 × 10⁷K

Applications and devices:

• Hydrogen bomb (thermonuclear weapon) - uses a fission bomb as a primary stage to create the high temperature and pressure needed to drive fusion in a secondary stage.
• Controlled fusion for power - research devices (magnetic confinement tokamaks, inertial confinement systems) aim to achieve net energy gain from controlled fusion for electricity generation; this remains an active area of research and development.

Thermonuclear Energy

Thermonuclear energy is the energy released in nuclear fusion reactions. Fusion reactions involve light nuclei (often isotopes of hydrogen such as deuterium and tritium) while fission reactions are typically initiated and sustained by neutrons interacting with heavy nuclei.

Fission vs Fusion

Solved Examples

Q1. In a nuclear reactor, what is the function of the moderator?

Solution: The moderator (heavy water D₂O, graphite) slows down fast neutrons to thermal energies so they can be efficiently absorbed by U-235 to cause further fission. 

Q2. In a nuclear fission reaction of U-235, energy released per fission is 200 MeV. How many fissions per second are needed to produce a power of 1 MW?

Solution: Power = 1 MW = 10⁶ W = 10⁶ J/s
Energy per fission = 200 MeV = 200 × 1.6 × 10⁻¹³ J = 3.2 × 10⁻¹¹ J 
Number of fissions = 10⁶ / 3.2 × 10⁻¹¹ = 3.125 × 10¹⁶ fissions/s 

Q3. The multiplication factor k in a nuclear reactor is maintained at:

Solution: In a nuclear reactor, k = 1, k is kept equal to 1 for a steady and controlled chain reaction. k < 1 means chain dies out. k > 1 means uncontrolled explosion (atom bomb principle). 

Q4.The D-T fusion reaction releases 17.6 MeV of energy. The energy released per nucleon is:

Solution: D has mass number 2, T has mass number 3 Total nucleons = 2 + 3 = 5 
Energy per nucleon = 17.6/5 = 3.52 MeV