8.4.3 Nuclear Fusion & Fission

Nuclear Fusion

• Fusion is defined as:

The fusing together of two small nuclei to produce a larger nucleus

• Low mass nuclei (such as hydrogen and helium) can undergo fusion and release energy
• When two protons fuse, the element deuterium is produced
• In the centre of stars, the deuterium combines with a tritium nucleus to form a helium nucleus, plus the release of energy, which provides fuel for the star to continue burning

The fusion of deuterium and tritium to form helium with the release of energy

• For two nuclei to fuse, both nuclei must have high kinetic energy
• This is because nuclei must be able to get close enough to fuse
  • However, two forces acting within the nuclei make this difficult to achieve

• Electrostatic Repulsion 
  • Protons inside the nuclei are positively charged, which means that they electrostatically repel one another

• Strong Nuclear Force
  • The strong nuclear force, which binds nucleons together, acts at very short distances within nuclei
  • Therefore, nuclei must get very close together for the strong nuclear force to take effect

• It takes a great deal of energy to overcome the electrostatic force, hence fusion can only be achieved in an extremely hot environment, such as the core of a star

Nuclear Fission

• Fission is defined as:

The splitting of a large atomic nucleus into smaller nuclei

• High mass nuclei (such as uranium) can undergo fission and release energy

The fission of a target nucleus, such as uranium, to produce smaller daughter nuclei with the release of energy

• Fission must first be induced by firing neutrons at a nucleus
  • When the nucleus is struck by a neutron, it splits into two, or more, daughter nuclei
  • During fission, neutrons are ejected from the nucleus, which in turn, can collide with other nuclei which triggers a cascade effect
  • This leads to a chain reaction which lasts until all of the material has undergone fission, or the reaction is halted by a moderator

• Nuclear fission is the process which produces energy in nuclear power stations, where it is well controlled
• When nuclear fission is not controlled, the chain reaction can cascade to produce the effects of a nuclear bomb

• The binding energy is equal to the amount of energy released in forming the nucleus, and can be calculated using:

E = (Δm)c²

• Where:
  • E = Binding energy released (J)
  • Δm = mass defect (kg)
  • c = speed of light (m s^-1)

• The daughter nuclei produced as a result of both fission and fusion have a higher binding energy per nucleon than the parent nuclei
• Therefore, energy is released as a result of the mass difference between the parent nuclei and the daughter nuclei

Part (a)

Step 1: Determine the binding energies on each side of the equation

Binding energy = Binding Energy per Nucleon × Mass Number

• • Binding energy before (U) = 235 × 7.59 = 1784 MeV
  • Binding energy after (Tc + In) = (112 × 8.36) + (122 × 8.51) = 1975 MeV

Step 2: Find the difference between the energies

• • Energy released = 1975 – 1784 = 191 MeV

Part (b)

Method 1

Step 1: Convert the energy released from MeV to J

• • 1 MeV = 1.60 × 10⁻¹³ J
  • Energy released = 191 × (1.60 × 10⁻¹³) = 3.06 × 10⁻¹¹ J

Step 2: Write down the equation for mass-energy equivalence

E = Δmc²

• • Where c = speed of light

Step 3: Rearrange and determine the mass defect, Δm

Δm = 3.4 × 10⁻²⁸ kg

Method 2

Step 1: Convert the energy released from MeV to u

Step 2: Calculate the mass defect, Δm

• • 1 u = 1.66 × 10⁻²⁷ kg

Δm = 0.205 × (1.66 × 10⁻²⁷) = 3.4 × 10⁻²⁸ kg