Nuclear Fusion In The Sun:Equations, Diagram,Causes,Steps

In this article we are going to discuss nuclear fusion in the sun reaction,equation,diagram,cause and steps elaborately.

We get light and heat energy from the sun. Hence the sun is the source of life on this earth. But here comes a question that how energy is originated in the sun. The answer is nuclear fusion. Through nuclear fusion reaction energy originates in the sun.

The core of the sun is the specific place where nuclear fusion takes place. Proton proton fusion is the specific type of nuclear fusion that is the reason behind the origination of energy. In the proton proton cycle a proton or 1H1 nucleus combines with the other proton to become a helium (2He4) nucleus.

As a result of this fusion process energy is radiated in the form of light and heat which in turn makes the sun hot. This produced energy radiates across the solar system. 99% energy is radiated from the core of the sun which is obtained from nuclear fusion in the sun.

Nuclear fusion in the sun from wikipedia

Nuclear fusion in the sun reaction

The rate of discharge of energy in the sun is 1026 joules per second. The temperature of the sun is about 20 million degrees and its age is approximately 5 x 109 years. So the total radiated energy by the sun through these years is extremely high. There is a confusion about the source of this energy.

In 1928 Atkinson and Houtermans suggested that this source is the combination of four protons that produce an alpha particle. According to them this can only be the source of this much amount of energy for this long period of time. The idea of cyclic nuclear reactions was proposed by them.

Thermonuclear reactions can produce this stellar energy – this concept was suggested by Hans Bethe in 1938. In these reactions protons are fused together to form helium nuclei. This cycle is termed as the proton proton cycle. This cycle is applicable for the stellar temperatures that are relatively low.

From this the concept of the red dwarf is obtained. The main source of energy in the sun and stars is the proton proton cycle that takes place at a low temperature. This is known as the red dwarf.

Proton proton cycle from wikipedia

Nuclear fusion in the sun equation

The equations of the proton proton cycle are written below:

(1) 1H1 + 1H11H2 + 1e0 + ν + 0.42 MeV

(2) 1H2 + 1H12He3 + γ + 5.5 MeV

(3) 2He3 + 2He32He4 + 2 1H1 + 12.8 MeV

There is a need of occurring equations (1) and (2) twice in this cycle of reactions. This can be yielded in two 2He3 nuclei in (3). The final result that can be obtained from these reactions is that four protons are combined to form an alpha particle.

In these reactions two positrons,two neutrinos and two  γ photons are also produced.

 4 1H1 2He4 + 2 1e0 + 2 ν + 2 γ

The total energy that gets released in this cycle is 24.6 MeV. Here the mass difference is 0.0286 u. As the neutrinos elope in these reactions the leftover energy is about 24.3 MeV after the nuclear fusion in the sun takes place in which four protons are fused into one helium nucleus.

Thus the concentration of the protons gets depleted whereas the concentration of helium builds up. This proton proton cycle of nuclear fusion in the sun occurs only if the kinetic energy of the protons or their temperature remains that high to overcome the mutual electrostatic repulsion.

Nuclear fusion in the sun diagram

The diagram of nuclear fusion in the sun is shown below:

nuclear fusion in the sun
Nuclear fusion in the sun from wikipedia

What causes fusion in the Sun

We know that nuclear fusion in the sun can be obtained when hydrogen atoms fused together. To get fused these atoms should come closer to each other. When two nuclei come closer the protons inside each of them try to repel each other as both are positively charged.

Nuclear fusion in the sun cannot take place if this problem is not able to be overcome. There are a number of conditions to get rid of this difficulty. They are-

The electrostatic repulsion force can be overcome by maintaining a high temperature which provides high energy to the hydrogen atoms.

  • 100 million kelvin temperature is required to cause nuclear fusion in the sun. This temperature is about six times hotter than the core of the sun.
  • Hydrogen does not behave like a gas at these temperatures,it behaves like a plasma. In the plasma state all the electrons are used to escape from the atoms and they move freely. It is a high energy state of matter.
  • The large mass of the sun helps it in achieving these high temperatures and this mass is compressed by the force of gravity in its core. Microwaves,lasers and ion particles should be used to achieve these temperatures.

The hydrogen atoms are squeezed together by the high pressure. The distance between each hydrogen should be 1×10-15m so that they can get fused together.

  • The large mass of the sun and the force of gravity are the two main factors that are used by the sun to squeeze the hydrogen atoms together in its core.
  • Intense magnetic fields,powerful lasers and ion beams are used to squeeze the hydrogen atoms together.

Deuterium – deuterium fusion will get a better response in the near future as extraction of deuterium from the sea water is easier than producing tritium from lithium. Deuterium is not radioactive but this deuterium- deuterium reaction will produce more energy.

Steps of nuclear fusion in the sun

The steps of proton proton cycle of the nuclear fusion in the sun are stated below:


At the first step of this cycle two protons get fused together in the sun. This pair of protons get separated from each other again most of the time.  But in a few cases one of the protons turns itself into a neutron with the help of the weak nuclear force.

A positron and a neutrino are also produced with the neutron in this reaction. This resulting proton-neutron pair is often referred to as deuterium.


After the first stage of the reaction a collision takes place between this produced deuterium and a third proton. A result of this collision a helium 3 nucleus and a gamma particle are produced. These released gamma particles are emitted from the core of the sun as gamma rays.

At last these rays are released as sunlight.


After that the collision between two helium 3 nuclei takes place in order to produce a helium 4 nucleus. In this reaction two extra photons are also produced as by-products of the reaction which escape out as two hydrogens.

At first a beryllium 6 nucleus is formed which in turn transforms into helium 4 nucleus as it is unstable in nature.

The total mass of the reactants that are the four protons is greater       than the mass of the helium 4 nucleus as a part of mass is converted into energy according to Einstein’s mass-energy relation,E=mc2. This excess energy is released in the form of light and heat from the sun.

This energy must have covered many layers of photosphere in order to escape from the sun. The amount of this released energy is very significant as the proton proton cycle occurs at a rate of 9.2 x 1037 times per second.  0.7 % of the total mass of the four protons is turned into energy.

4.26 millions metric tons of mass are turned into energy per second. From the mass energy relation of Einstein it can be stated that these 4.26 millions of metric tons of matter gives 3.8 x 1026 joules of energy per second.


The detailed facts of the nuclear fusion in the sun equipped with the exact diagram,equations of the proton proton cycle,steps of the cycle are described in this article.

Read more about 5 Important Stages Of The Sun?

Ankita Biswas

Hi...I am Ankita Biswas. I have done my B.Sc in physics Honours and my M.Sc in Electronics. Currently, I am working as a Physics teacher in a Higher Secondary School. I am very enthusiastic about the high-energy physics field. I love to write complicated physics concepts in understandable and simple words. Let's connect through LinkedIn:

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