Nuclear Fusion in Stars

This topic is part of the HSC Physics course under the section Origins of the Elements.

HSC Physics Syllabus

• analyse and apply Einstein’s description of the equivalence of energy and mass and relate this to the nuclear reactions that occur in stars (ACSPH031)

• investigate the types of nucleosynthesis reactions involved in Main Sequence and Post-Main Sequence stars, including but not limited to:

– proton–proton chain
– CNO (carbon-nitrogen-oxygen) cycle

How do stars produce energy?

This video discusses three main types of nuclear fusion that occur in stars: proton-proton chain, CNO cycle and triple alpha process.

Nuclear Fusion

Stars, including our Sun, produce energy via nuclear fusion. Nuclear fusion is the process in which atomic nuclei physically combine to form one or more different atomic nucleus and additional sub-atomic particles such as neutrons.

Nuclear fusion obeys energy-mass conservation but requires the application of energy-mass equivalence.

Energy and Mass Equivalence

In classical physics, the law of energy and mass conservation underpins many common phenomena such as the collision between objects, acceleration of rockets during its launch and all chemical reactions (formation of product from reactants)

Einstein proposed that mass and energy are in fact interchangeable. Mass can be converted into energy and energy can be converted into mass. As a result, each quantity does not need to be conserved in its own form as they can inter-convert.

The energy and mass equivalence is governed by the equation:

$$E=mc^2$$

• Where E is energy in Joules (J)
• m is the rest mass of a particle or object in kilograms (kg)
• c is the speed of light in m s-2

Alternatively, this equation can be used by using the following units:

• E in MeV
• in MeV c^(-2)

Mass can be converted from kg to atomic mass unit (u) by dividing by 1.661 xx 10^(-27).

It can be converted from u to MeV c^(-2) by multiplying by 931.5.

This form of mass and energy conservation and conversion is commonly observed in nuclear reactions and situations where high-speed particles collide.

Proton-proton Chain

The proton-proton chain is the simplest form of nuclear fusion that occurs in main-sequence stars. Proton-proton chain involves the fusion between 4 hydrogen nuclei (H-1) to form a helium nucleus (He-4).

The atomic mass of one hydrogen atom is roughly 1.008 u. When four hydrogen atoms combine, the total mass of resultant products should add up to 4.032 u due to mass conservation.

The steps that take place during the proton-proton chain are detailed in the following diagram.

However, the resultant helium nucleus weighs less than 4.032 u which means the lost mass has converted into energy. Using Einstein’s equation and information from the periodic table, the energy produced is

The overall reaction of the proton-proton chain can be summarised by the following nuclear equation.

Four protons are combined to form a He-4 nucleus, two electron neutrinos, two positrons and two gamma photons.

Carbon, Nitrogen, Oxygen (CNO) Cycle

CNO cycle is a series of nuclear fusion reactions that occur in main sequence stars like our Sun. The cycle involves isotopes of carbon, nitrogen and oxygen, and more importantly the production of a helium nucleus from the inclusion of four protons in different parts of the cycle.

Similar to the proton-proton chain, a He-4 nucleus is formed every one CNO cycle. In contrast, more energy is produced every time a He-4 nucleus is formed from CNO cycle than from proton-proton chain.

The application of energy-mass equivalence in CNO cycle is identical to that in the proton-proton chain. The energy is derived from the mass difference between four protons and the result product of nuclear fusion – helium nucleus.

How Do Main-sequence Stars Produce Energy?

Main-sequence stars like our Sun produce energy using the proton-proton chain and the CNO cycle.

However, the proportion of total energy produced from each nuclear fusion process depends on the core temperature of a main-sequence star. This is because nuclei involved in the CNO cycle experience greater electrostatic repulsion due to their greater charge. A higher core temperature is required so these nuclei have sufficient kinetic energy to overcome the repulsion and collide to undergo nuclear fusion.

CNO cycle requires 15 MK (mega-Kelvin) to start and only becomes the prominent source of helium nuclei when the temperature reaches 17-18 MK.

For example, our Sun’s core is about 15.7 MK and only 1.7% of helium nuclei are made from CNO cycle. Therefore, the majority of energy produce by the Sun is due to the proton-proton chain.

Proton-proton chain’s energy production rate is proportional to the temperature to the power of four (T4) whereas CNO cycle is to the power of 17 (T17).

A star remains as a main sequence star as long as there are available hydrogen nuclei to be ‘burned’ to form helium.

Triple Alpha Process

The triple alpha process is a nuclear fusion process where three helium nuclei are combined to form a carbon-12 nucleus (C-12). The C-12 nucleus can sometimes capture an additional He-4 nucleus to produce an oxygen-16 nucleus (O-16).

The triple alpha process occurs in post-main sequence stars. This is because the triple alpha process can only occur when the star’s core temperature is greater than 100 MK. The high core temperature gives nuclei sufficient kinetic energy to overcome their much greater electrostatic repulsion.

Proton-proton chain and CNO cycle cause He-4 nuclei to accumulate in the core of main-sequence stars. When a main-sequence star evolves into its next stage (e.g. red giant), the core temperature of the star becomes sufficient for the triple alpha process to take place. This way, the star makes use of the large quantity of He-4 nuclei to synthesise heavier elements and produce more energy.

Other Nuclear Reactions in Post-main Sequence Stars

Besides the triple alpha process, there are numerous other nuclear fusion reactions that occur in post-main sequence stars such as red giants and supergiants.

Nuclear reactions in stars can produce heavier elements up to iron (Fe). The synthesis of elements heavier than iron will not produce energy because these elements have increasing smaller binding energies per nucleon with increasing atomic mass.

As the core temperature of a post-main sequence star continues to increase, collision between carbon nuclei become possible to form either neon, sodium or magnesium (the details of these reactions are not essential for HSC Physics).

• Two carbon-12 nuclei can combine to form a neon nucleus, emitting a helium nucleus in the process.

• Two carbon-12 nuclei can combine to form a sodium nucleus, emitting a proton (hydrogen-1) in the process.

• Two carbon-12 nuclei can combine to form a magnesium nucleus, emitting a photon in the process.

• Helium nuclei can collide with existing oxygen-16 nuclei (created from triple alpha process) to form more neon, emitting a photon in the reaction.

• Neon can fuse with helium nuclei to form magnesium

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