Stars and Fusion – Learn

Einstein’s Equivalence of Mass and Energy

Early calculations and observations of the Sun gave some unexpected results – an unusually large amount of energy was being released for every atom in the sun. When compared to chemical reactions, there was approximately 100 million times more energy released!

When Einstein developed his theory of relativity Physicists began to understand what was going on in the Sun. A central element of Einstein’s theory is his mass-energy equivalence equation: E = mc2. A loose interpretation of this equation indicates that there is a huge amount of energy locked up in mass. This comes about as a result of the factor of c2. A huge amount of energy is being released from the Sun and it was hypothesised that somehow the reactions in the Sun were making use of Einstein’s mass-energy equivalence equation.

To better understand what causes the huge amount of energy released from the Sun we need to understand what is happening in the core of the Sun and what allows these conditions to occur. Firstly, stars are comprised of mostly hydrogen and helium and form when these gases collapse due to the gravitational attraction between the atoms. This collapse results in a loss of gravitational potential energy which must be transformed into some other form of energy – thermal energy. In the Sun’s core, temperatures in the order of millions of degrees provide enough energy for the electrons in the Sun to be no longer bound to the nuclei. It was concluded that the conditions in the centre of the Sun allowed for hydrogen nuclei to fuse and form helium nuclei. This process is known as nuclear fusion and releases huge amounts of energy as a result of some mass loss during the nuclear reaction.

Nucleosynthesis

Stars begin their lives as protostars when clouds of gas and dust start to collapse under their own gravitational force. The loss of gravitational potential energy is converted into heat energy and temperatures of around 10 million degrees are reached which start off a chain of nuclear reactions. These nuclear reactions release extra heat which, due to the outward radiation force eventually balance the collapse of the star due to gravity. At this point the protostar becomes a main sequence star and its lifetime is dependent on the mass of the star – millions of years for massive stars, billions of years for stars like our Sun and tens of billions of years for lower main sequence stars.

During the main sequence stage of a star the energy that is generated comes from the fusion of hydrogen nuclei into helium nuclei – this process is called nucleosynthesis. The two main fusion processes that occur in stars are the proton-proton (P-P) chain and the carbon-nitrogen-oxygen (CNO) cycle reactions. Both the PP chain and the CNO cycle combine four hydrogen nuclei into one helium nucleus. The energy that is released is due to the mass defect that occurs in the fusion process between reactants and products.

In both reactions the net nuclear equation is: 4_{ 1 }^{ 1 }{ H }\rightarrow _{ 2 }^{ 4 }{ He }+2{ e }^{ + }+2v+2\gamma

Proton-Proton (P-P) Chain Reaction

In main sequence stars with temperatures below 18 million degrees kelvin, the proton-proton chain reaction is the main process that generates energy in the core of the star. The reaction proceeds by:

  • two separate fusions of protons produce deuterium, which has one proton and one neutron. The neutron arises because one of the protons decays by positron emission to a neutron. An electron neutrino is also emitted.
  • each of the two deuterium nuclides now undergoes fusion to helium-3 by incorporating another proton. Most of the energy is released from this reaction as a gamma ray.
  • lastly, the two helium-3 nuclides undergo fusion to helium-4, which is stable. Two protons are released back into the star.

This process is illustrated below:

Carbon-Nitrogen-Oxygen (CNO) Cycle Reactions

In massive stars the more complex CNO cycle reaction dominates. Carbon acts as a catalyst in the reaction as it is transformed into nitrogen and then oxygen before returning back to carbon to start the cycle again.

This process is illustrated below: