Nuclear Fusion: Definition, Occurence, Examples, Energy Generation in Stars

Ever looked at the sun on a terribly humid day and wondered where is all that heat coming from? The answer for this is nuclear fusion. The stars we see at night have been formed as a result of a phenomenon called the Stellar life cycle; when dust and gas particles attract to each other due to gravity, they accumulate and form a star. In both of these examples, energy is released as a result of changes inside a nucleus; a process called nuclear fusion. In a nuclear fusion reaction, more energy is released in comparison to a nuclear fission reaction. In this article, we will explore nuclear fusion in detail.

Table of Contents

• What is Nuclear Fusion?
• Stellar Life Cycle
• Practice Problems of Nuclear Fusion
• FAQs of Nuclear Fusion

What is Nuclear Fusion?

When two lighter nuclei fuse together to form a heavier nucleus, it is termed as a fusion reaction. The difference in mass between the parent and daughter nuclei is called binding energy. In a fusion reaction, since the daughter nucleus formed is more stable, it has higher binding energy per nucleon than the parent nuclei. A good example would be the fusion of two hydrogen nuclei to form a helium nucleus, which happens in the sun.

₁H¹ + ₁H¹ → ₁H² + e⁺ + v + 0.42 MeV

e⁺ + e^- → γ + γ + 1.02 MeV

₁H² + ₁H¹ → ₂He³ + γ + 5.49 MeV

₂He³ + ₂He³ → ₂He⁴ + ₁H¹ + ₁H¹ + 12.86 MeV

       e⁺ → Positron

       e^- → Electron

   ₁H¹ → Hydrogen nucleus

    ₁H² → Deuterium nucleus.

    ₁H³ →Tritium Nucleus.

       v → Neutrino

       γ → Gamma rays

  Both deuterium and tritium are isotopes of hydrogen.

Stellar Life Cycle

• Stars are formed due to slow accumulation of cloud dust from H and He.
• If a molecular cloud is able to gather enough material, then that material, under the influence of gravitational attraction, begins to accelerate inwards and collision occurs.
• Due to the collision, heat is produced, which starts the nuclear fusion process and the star begins to fuse H into He. This is how a star is born. 
• The energy liberated during the fusion process tries to expand the star; a process called thermal pressure. But the gravity which is acting inwards does not let the star expand. So, the star for the most part of its life, is in equilibrium,.i.e the thermal pressure and gravity balance each other. 
• When the star uses up most of its fuel, i.e H, the gravitational force dominates the thermal pressure and the core of the star shrinks.
• Due to the shrinking of the core, the temperature of the star rises, and hence, the rate of nuclear fusion also increases.
• When the rate of nuclear fusion increases, the outward pressure surpasses the force of gravity and the star starts to expand and then it slowly moves into a phase called the red giant.
• When all of the hydrogen is used up, the gravity again becomes dominant, and the core shrinks even more. Due to this the temperature becomes very high, and the fusion of helium starts. He fuses into carbon which in turn fuses into oxygen. Therefore, carbon and oxygen are synthesized. 
• There will come a time when all of the He will be used up. Then the thermal pressure will be minimized, and the gravity will become so dominant that the star itself starts to collapse. 
• If the mass of the core of the star is less than 1.4 M₀(Chandrasekhar limit) where M0 is the solar mass, the star will become a white dwarf (A dense star about the size of a planet).
• If the mass of the core is in between 1.4 M₀ and 3 M₀, the gravity will be so high that the star collapses on itself and a huge explosion called a supernova occurs. Supernova is the brightest event in the whole universe. 
• In a white dwarf, the electrons surrounding the nucleus will push against each other and stop the gravity to crush it. This is called electron degeneracy pressure.
• In the case of a neutron star, the gravity is so high that the electrons get crushed into the protons, and they combine to form neutrons. So there will be a core made up of only neutrons. 
• If the mass of the core is greater than 3 M₀, the gravity is so intense that even the neutrons will get crushed, and a black hole will form. 

Practice Problems of Nuclear Fusion

Q1) What is X in the following reaction? 

₁H² + ₁H¹ →  ₂X³ + γ + 5.49 MeV

Solution) ₁H² + ₁H¹ → ₂He³ + γ + 5.49 MeV

Q2) What is Y in the following reaction? 

  ₁H¹ + ₁H¹ → ₁Y² + e⁺ + γ + 0.42 MeV

Solution)  Y is ₁H².

Q3) Complete the following reaction? 

₆C¹² + ₂He⁴ → ? + γ 

Solution) ₆C¹² + ₂He⁴ → ₈O¹⁶ + γ 

Q4) Calculate the total energy released in the nuclear fusion reaction of the sun?

Solution) ₁H² + ₁H² → ₁H² + e⁺+ γ + 0.42 MeV

  e⁺ + e^- → γ + γ + 1.02 MeV

₁H² + ₁H¹ → ₂He³ + γ + 5.49 MeV

₂He³ + ₂He³ → ₂He⁴ + ₁H¹ + ₁H¹ + 12.86 MeV

Total energy = 0.42 + 1.02 + 5.49 + 12.86 = 19.79 MeV

FAQs of Nuclear Fusion

Question1. The binding energy per nucleon of the daughter nucleus is more than that of the parent nucleus in a fusion reaction. Why?
Answer. The daughter nucleus is more stable, hence more binding energy per nucleon.

Question2. Define nuclear fusion?
Answer. When two lighter nuclei fuse to form a heavier nucleus, it is called a fusion reaction.

Question3. Explain how stars are born?
Answer. Dust slowly accumulates after falling under the influence of gravity, and begin to accelerate inwards and collision occurs. Due to the collision, heat is produced, which starts the nuclear fusion process and the star begins to fuse H into He. This is how a star is born.

Question4. Write the fusion reaction of deuterium nuclei forming helium.
Answer.  ₁H² + ₁H² → ₂He⁴ + Energy.