Nuclear Fusion in the Sun Explained Perfectly by Science

Fact about the Sun
Nuclear fusion is the source of Sun's phenomenal energy output. The Hydrogen and Helium atoms that constitute Sun, combine in a heavy amount every second to generate a stable and a nearly inexhaustible source of energy.
Sun - The Ultimate Nuclear Fusion Reactor
Every second, the Sun fuses 620 billion Kg of Hydrogen nuclei (protons) into Helium, to produce 384.6 trillion trillion Joules of energy per second. This is equivalent to the energy released in the explosion of 91.92 billion megatons of TNT per second.
Sun is our star and the source of all energy on Earth. Solar energy sustains all the life on our planet through photosynthesis, and sets the rhythm of our climate and seasons. Since ages, people have pondered about the source of Sun's extraordinarily high energy output which amounts to 3.846 × 1026 Joules of energy, per second. What endows stars like our Sun with this almost endless energy? Today, thanks to years of painstaking research, we know the answer. Nuclear fusion (the fusing together of atomic nuclei into heavier nuclei at high temperatures) is the key which unlocks almost limitless power for the Sun.
Nuclear Fusion in the Sun's Core
Before we delve deeper into the heart of the Sun, the most sophisticated thermonuclear reactor we know, some basics must be clarified.
The Atomic Nucleus
This small introduction is for those, who are not familiar with atomic physics. Everything is made up of atoms. They are the smallest indivisible units of any object. The central core of an atom is the nucleus, which is quite dense and packed with most of the atom's mass, with electrons revolving around it.
What is Nucleus?
The nucleus consists of two types of particles - protons and neutrons. A proton has a unit positive electric charge (1.6 x 10-19 Coulomb), while the neutron is neutral. A type of an atom is decided by the number of protons in it.
There are 92 different types of naturally occurring atoms. Hydrogen is the simplest type of atom that you could think of. Its nucleus is just a proton. Every atom is denoted by an abbreviation of its chemical name. When I want to denote Hydrogen, I use the symbol 'H'.
Atomic Weight
Atomic weight is the total number of protons and neutrons in the nucleus, while atomic number is the number of protons or electrons that make the atom. Hydrogen is denoted as 11H, where the number in the superscript is the atomic weight and the number in subscript is the atomic number. Since the thermonuclear reactions occur at the level of a million Kelvins, all atoms are stripped of their electrons in the solar core.
What is Nuclear Fusion?
hydrostatic equilibrium
Sun is a star and all stars are big balls of gas, primarily made up of gargantuan amounts of Hydrogen and Helium. About 75% of the Sun is made up of Hydrogen, while the rest is mostly all Helium.
What Makes Sun, Stable?
Solar interior witnesses a constant tussle between the crushing gravitational force and thermal pressure, generated by nuclear fusion in the core. The Sun is stable due to the hydrostatic equilibrium achieved between the self-gravity of the Sun and the thermal pressure generated by fusion in the core.
How Does Fusion Take Place?
Fusion is a process by which rapidly-colliding nuclei, like those of Hydrogen, fuse together at very high temperatures, to form nuclei of higher atomic weight. In this process some mass is lost and converted into energy. That is the secret of Sun's energy production. To put it simply, Sun generates its energy, primarily through the fusion of four Hydrogen nuclei to form a Helium nucleus.
The amount of energy obtained from conversion of 1 gm of matter into energy (by Albert Einstein's celebrated equation, E = mc2) would be roughly 9 X 1013 Joules. So matter is just a form of energy. They are two manifestations of the same thing. All matter that makes up the Earth, along with the stuff that we are made of - Carbon, Nitrogen, Oxygen, was forged in the cores of high mass stars that burned and died long before the Sun.

For the past 4.57 billion years, since its birth, the Sun has been steadily fusing Hydrogen into Helium (a stage known as the Main Sequence in stellar physics parlance) and it will continue to do so for the next 5.43 billion years. In this entire time, the Sun has burnt Hydrogen, equivalent to about 100-Earth masses.
Where Does Nuclear Fusion Occur in the Sun
interior of the sun
Nuclear fusion occurs in the Sun's core, which, not coincidentally, is also the hottest part of its whole constitution. The heart of the Sun has a temperature close to 15.7 million Kelvin. The total radius of the Sun is 6.955×105 km (about 109 times radius of Earth). Its core extends from the center to about 1.391 X 105 Km.
Let me explain why fusion occurs only near the center. It can be easily understood, if you try to understand how the Sun formed.

Stars like the Sun are thermonuclear fusion reactors. Fusion is a merger of smaller nuclei into heavier ones, releasing a tremendous amount of energy in the process. However, Hydrogen nuclei, which are protons, do not fuse easily. The reason for that is a fundamental fact of nature, which is, 'Like charges repel each other'.
The phenomena of a positively charged proton repelling from another one of its kind, because of the same charge is called Coulomb repulsion. Ergo, nuclear fusion can only occur at a high temperature, at the central core of the Sun. Sun's core is hottest due to its phenomenally high density (150 gm/cm3), a result of its compression under self-gravity.

Nuclear fusion is only possible when the repulsion between protons (Hydrogen nuclei) is overcome. For that to happen, energy and temperature at the Sun's core has to be substantially high. However, nature has arranged it such, that the fusion in Sun's core can occur at a much lower temperature, than that required to overcome Coulomb repulsion. How does nature pull off this trick? The answer lies in quantum mechanics.
Nuclear Fusion is Possible Due to Barrier Penetration
The reason why protons with energy lesser than that required to overcome Coulomb Repulsion fuse, is barrier penetration. It is a quantum physics concept. Consider the following analogy. Imagine an adamant old man, trying to scale a wall. He doesn't have the energy or the tools to climb it. Even so, he is of the opinion that if he keeps banging and ramming into the wall, one day it will give in and he will be on the other side by tunneling through.
The chances of that happening in the Classical (Non-Quantum Mechanical) world is zero. However, if our old man was the size of a proton (< 10-15m), and the wall represented the Coulomb energy required to overcome repulsion, then if he keeps hitting the wall, there is a chance (small finite probability) that he will tunnel through.
In the weird, sub-microsopic world of quantum mechanics, there is always a finite probability that the protons will fuse together at an energy that will be, lower than required energy to climb the Coulomb repulsion hill.

Since the probability of tunneling through Coulomb barriers is very low, fusion processes in low mass, relatively cooler stars like Sun, occur very slowly. A crucial step in the nuclear fusion process, which is the fusing of Hydrogen (11H) into Deuterium (21D) also has a very low probability of occurrence. That's why, stars like the Sun burn or rather fuse their Hydrogen fuel into Helium at a very low rate and have long lifespans. Long-lived G-type main-sequence stars like the Sun can, therefore, have a high probability of harboring life around them on some revolving planet, as they last long enough for life to evolve.
What Happens During Fusion inside the Sun?
The type of nuclear fusion reactions that occur inside a star, are entirely dependent on the core temperature. In the Sun, with a core temperature close to 15.6 million Kelvin, the predominant pathway, by which more than 99% of solar energy is produced (through conversion of hydrogen into helium nuclei), is the Proton-proton (p-p) chain reaction. The other primary pathway which produces about 0.8% of Solar energy is the CNO cycle.
Solar Nuclear Fusion Process #1: The Proton-Proton (p-p) Chain Reaction
solar nuclear reactions
This is the dominant fusion process in the Sun. This phenomenon is possible due to tunneling or barrier penetration. There are many alternative ways in which the proton-proton chain reaction itself can occur. Besides the prime p-p pathway, other associated pathways are h-e-p and p-e-p, explained.
Step 1a
The process begins with the fusion of two hydrogen nuclei (protons) to form Helium-2 or a diproton (22He).
Step 1b
Further, the diproton undergoes beta decay (proton gets converted into a neutron, along with the release of an electron neutrino and a positron, which is the antiparticle of the electron) to get converted into deuterium, along with the release of a positron and an electron neutrino. Beta decay of the diproton being an extremely rare event, this is the step that causes maximum delay in the fusion process, extending the lifespan of the Sun.

22He → 21D + e+ + νe
Summing up, this is what happens in the first step, in totality -

11H + 11H → 21D + e+ + νe + 0.42 MeV

(*Electron volt is a measure of energy. One electron volt (eV) is the energy gained by an electron as it passes through a potential difference of 1 Volt.)

When matter and antimatter, come together, they get annihilated to create pure energy. The positron created in the beta decay gets annihilated, when it comes in contact with an electron, to release two high-energy gamma ray photons.

e- + e+ → 2γ + 1.02 MeV
PEP Reaction
Very rarely, the production of Deuterium (D) might also occur through another process, known as the proton-electron-proton (p-e-p) reaction. It involves electron capture and works as follows:

11H + e- + 11H → 21D + νe

Although it is 400 times more likely that Deuterium will be created by the p-p pathway, the p-e-p reaction does occur rarely, creating high-energy neutrinos.
Step 2
The fusion of Deuterium with a Hydrogen nucleus (proton) leads to the production of a light Helium isotope (3He), besides releasing a gamma ray (an electromagnetic wave, with a frequency greater than 1019 Hz).

21D + 11H → 32He + γ + 5.49 MeV
Step 3
After the previous stage, there are more than one ways in which the reaction may proceed. There are four prime paths: pp1, pp2, pp3, and pp4. Let us look at each path in detail.
ppI Pathway: Light Helium Fusion
chain reaction
This is the dominant pathway among the four possible alternative paths that the reaction can take after creation of 3He when the temperature of the core ranges between 10 million to 14 million Kelvin. It involves the fusion of two light helium nuclei to produce two protons (Hydrogen nuclei), along with the release of 12.86 Kelvin of pure energy. The frequency of pp1 pathway is around 86%.

32He + 32He → 42He + 2 11H + 12.86 MeV

In totality, the energy released by the pp1 reaction is 26.22 MeV.
ppII Pathway: Lithium Burning
At temperatures between 14 million to 23 million Kelvin, the ppII branch is dominant. Here are the prime reactions that constitute it.

32He + 42He → 74Be + γ

74Be + e-73Li + νe + 0.861 MeV/0.383MeV

73Li + 11H → 2 42He

Since the Sun's core temperature has a maximum around 15 million Kelvin, the ppII pathway only occurs with a frequency of 14%.
ppIII Pathway: Beryllium Boron Transmutation
Since this type of reaction requires a temperature in excess of 23 million Kelvin, its frequency is only 0.11%. The pathway involves transmutation between Beryllium (Be) and Boron (B) isotopes. Here are the steps:

32He + 42He → 74Be + γ

74Be + 11H → 85B + γ

85B → 84Be + e+ + νe

84Be → 2 42He
ppIV Pathway: Hep Reaction
Theorized, but not yet observed, this Helium-Proton fusion pathway is extremely rare. The pathway consist of just one reaction. It consists of a direct fusion of a Helium-3 nucleus with a proton.

32He + 11H → 42He + e+ + νe + 18.8 MeV

The difference between the 'fusing masses' (the four protons) and 'fused mass' (Helium-4) is 0.7% of the total mass of 4 protons, which is converted into energy. The total energy produced by the fusion of 4 protons through these processes is 26.73 MeV.
Solar Nuclear Fusion Process #2: Carbon-Nitrogen-Oxygen (CNO) Cycle
cno cycle
This nuclear fusion process occurs very marginally in the Sun, but is the dominant fusion pathway in stars 1.5 times more massive, than our Sun. This process also fuses four protons into a Helium nucleus, by using Carbon (C), Nitrogen (N) and Oxygen (O) nuclei as catalysts. There are several alternative CNO pathways that can lead to Helium-4 production. This process produces only 0.8% of the Sun's total energy output. Like p-p chain reaction, the CNO cycle has several alternative paths, but the dominant one, occurring in the Sun, is primarily CNO-I. The reactions constituting the cycle are as follows:

Step 1: 126C + 11H → 137N + γ + 1.95 MeV

Step 2: 137N → 13C6 + e+ + νe + 1.2 MeV (Half-life: 9.965 min)

Step 3: 136C + 11H → 147N + γ + 7.54 MeV

Step 4: 147N + 11H → 158O + γ + 7.35 MeV

Step 5: 158O → 157N + e+ + νe + 1.73 MeV (Half-life: 122.24s)Step 6: 157N + 11H → 126C + 42He + 4.96 MeV

The end products of both the processes are same. However, CNO cycle is dominant in stars with stellar cores much hotter than that of Sun (in the range of 13 Million Kelvin). However, despite occurring at higher temperature, overall energy released through the whole reaction is again 26.73 MeV, which is round about the same as p-p cycle.

The energy released through gamma rays and the kinetic energy of the particles contributes to generation of thermal pressure in the solar interior, effectively balancing it with the gravitational pressure to maintain an overall steady state. It takes 10,000 to 170,000 years for a photon to travel from the Sun's core, to its surface. On its way, the gamma ray photons emitted in the fusion reactions are converted into visible light, infrared and ultraviolet photons, as they reach the photosphere.
The multiple processes involved in fusing Hydrogen into Helium are testimony to the way nature always has many alternative ways to achieve the same result. Redundancy seems to be built into the fabric of the cosmos, for some reason. Stars are the furnaces that cook the stuff we are made of. Next time you see a sunrise, you will be able to appreciate the beauty of the glowing hot ball of fire, even more, as you now know what goes on in its very heart.