Thermonuclear Fusion

Each second, the sun transforms 700 million tons of hydrogen gas into 695 million tons of helium gas through the nuclear reaction of fusion. The remaining 5 million tons of matter (about 600 times the weight of water flowing over Niagara Falls in one second) escape as pure energy. I recall several visits to the Wright Patterson Air Force Base in Dayton, Ohio. While many might first think of stored alien and UFO artifacts being there, I was more interested in the Air Force Museum. While I would wander through the hangars, I was always most impressed by the B-52 Stratofortress. Its wingspan is 181 feet, and therefore needed wheels on the wingtips to keep them from dragging on the runway concrete. Underneath this huge bomber was a Mark 24 thermonuclear bomb. This device weighed an incredible 42,000 pounds, and when dropped from the bomber, would cause the plane to hop up almost 300 feet in a sudden release of weight. The yield of this bomb was 15 megatons! If a 42,000 pound bomb produces 15 megatons of explosive power, imagine what 5 million tons explosive power is like ... and this is released every second.

The thermonuclear powerhouse is contained - and maintained - by the extreme conditions that exist in the sun's core: temperatures of 15,000,000 K and pressures about 250,000,000,000 times that of earth's atmosphere. Since the core holds approximately 50% of the sun's mass in just 1/64th of its volume, the sun is saved from gravitational collapse only by the outward pressure exerted by the stupendous outward energy pressure generated in the core.

If we are to learn about the Universe, the place to begin is at home, and there is no better place than the sun. While you are welcome to read detailed textbook material, I have chosen the most important information about solar physics to present in these pages. We will start first events in the interior of the sun, the interesting information on the energy escapes, and finally to phenomenon at the surface which have dramatic effects on the Earth. Keep in mind that astronomers and physicists alike are fairly certain about the process of thermonuclear fusion, but exact details are unclear and certainty as to the rate of hydrogen burning lingers.

Big Picture First

The Sun creates light. This is a defining feature of stars. All starts create light, and they create light as the result of nuclear fusion. This light is different from a light bulb that incandesces as the result of electricity heating a filament, or a light bulb that fluoresces when the gas inside the tube is ignited by electricity. The Sun actualy creaes light from a non-electrical process, and sunlight is different from light bulb light. A light bulb releases only one kind of light ... visible, and some infrared. The Sun releases all of the part of the Electromagnetic Spectrum, from the very long wavelength Radio Waves, to mid-length Visible Light, to the very short wavelength Gamma Rays. However, the Sun ONLY makes GAMMA RAYS, and these rays are ONLY made IN THE CORE. The Sun is a gigantic thermonuclear bomb where Four Hydrogen protons are fused together into One Helium nucleus, and gamma rays are released. This process is called Thermonuclear Fusion, and any star that has the Hydrogen fusion reaction as the primary energy source is said to be on the Main Sequence of the HR Diagram (you'll definitely learn about this later). The gamma rays that are made in the core have to escape, but during their outward journey, they collide with particles that are in the way. With each collision, a little bit of energy is lost. While all forms of electromagnetic radiation travels at the speed of light, some gamma rays escape quickly because they have fewer collisions. Other gamma rays may take longer to escape because they have more collisions, and thus they lose much energy and drop down to visible, infrared, or even lower energy forms of electromagnetic radiation. The details of this entire process are found in the rest of this section of the course.

Energy Production

 

Astronomers have learned much about the working of the Sun from their study of the spectrum which the sun's like produces. As we learned in the earlier unit about electromagnetic radiation, the visible portion of the solar spectrum has dark lines called "absorption lines." Conditions within the Sun cause electrons that are normally at a resting star near their nuclei to gain energy and jump to a higher energy state. When an electron is excited up to a higher energy orbital, it absorbs a photon of a specific energy --- that of the difference between the two orbitals for that specific atom. If enough electrons absorb photons at a given energy, an absorption line is formed. Given enough energy, electrons can jump more than one level at a time. When the electron drops to a lower energy orbital, the photon is released. The result is an emission line. Each kind of atom has a different kind of ladder with a different number and variety of energy jumps available. As a result, each kind of atom or ion has a different absorption or emission spectrum.

When astronomers looked at the absorption lines from the Sun, they discovered that the Sun is composed of 91% Hydrogen and 9% Helium (recent work has refined these numbers such that it is presently believed that the Sun is 70% Hydrogen, 28% Helium, and 2% other elements). This adds up to 100%, meaning that all of the other elements in the Sun comprise small fractions of a percent, with oxygen leading, then carbon, neon, nitrogen, and 70 or more others. A hydrogen atom has one nuclear particle (a proton) and one electron. Helium has 4 nuclear particles (2 protons and 2 neutrons) and 2 electrons. {A little side note here. I received a very nice postcard from a man in Salem, Oregon who caught a mistake that I had made in the previous paragraph. I had typed the presence of 4 electrons in a helium atom instead of 2. The postcard writed went on to praise the course material, and I was genuinely appreciative of the compliment, but felt so foolish for having typed in such an obvious error. The postcard made me feel part of a collabortive effort to deliver the best work that I can for my students - my thanks to the mystery reader in Oregon.} Many more elements are burning in gaseous form in the Sun, but only comprise less than 0.2% of the mass. We know of their presence by the spectral pattern on the Absorption Spectrum of the Sun. Deep inside the core of the sun where temperatures and pressures are sufficiently high, hydrogen atoms are stripped of their electrons and the interior of the sun exists as free electrons and atomic nuclear protons in a soup called "plasma". The high heat created by gravitational pressure causes these protons to "vibrate" rapidly and bounce off other protons. To understand what happens to these protons, one must know a little bit about the four "Forces of Nature" that act over a distance. (A great deal of mental effort has been expended to understand the relationship between these forces and unite them into one overall theory called, "The Grand Unification Theory." To date, no one has been able to describe such a GUT theory, but perhaps in your lifetime one will succeed and you can see where a Nobel Prize will go. Meanwhile, just what are these forces of Nature, and how do they battle in a star?)

The 4 Forces of Nature

The four forces of Nature, from the weakest to the strongest are Gravity, Weak, Electromagnetic, and Strong. The interior of our Sun is a great battleground between these four forces. The result of this battle is the generation of light and heat to which we owe our very existence. The best known of all the forces is "gravity," first mathematically described by Isaac Newton in the mid-1600's. It is also the weakest of the four forces. It is a force that cannot be neutralized, acts over all distances in space, and draws all matter to other matter ... whether it be atoms to atoms or galaxy to galaxy. It is the driving force of the Universe, responsible for bringing about the formation of stars and maintaining order in galaxies.

The second force is called the "Weak Force," and it acts only across the diameter of an atom. It is involved in radioactive decay in which one kind of atom changes into another kind with a release of energy.

The third force is the electromagnetic force that, like gravity, acts over all distances, but unlike gravity, has two associated directions. The electric charge can be either positive or negative (the charges being carried by protons or electrons respectively), and thus this force can be neutralized. A normal atom has equal numbers of protons and electrons, and thus equal positive and negative charges. Such a neutral atom, from a distance is safe. Only when the charges are out of balance can be feel the electromagnetic force directly. On an atom-to-atom basis this force is 10e35 times stronger than gravity, and accounts for the painful sensation one feels when stupidly inserting a finger into a wall socket.

Finally, there is the "strong force" which also acts across the distance of an atom, and like the name implies, is the most powerful of the four forces. It is responsible for holding positively charged protons together in the nucleus against the repulsive force of the particles. I continue to be amazed at the relatively few, if any, high school students that ever ask their chemistry teachers, "what holds those positively charged protons together in the nucleus when magnetic charges should blow any nucleus larger than hydrogen apart?" The typical thought is that the negative charge of the electrons counters the positive charge of the proton, but that negating effect only balances the charge of the atom, and has nothing to do with the forces in the nucleus. We can be thankful for the presence of the strong force, for without it, no molecule larger than individual hydrogen ions could exist.

Now, as we mentioned earlier in this unit, the presence of limb-darkening on the Sun evidences the properties of gas and pressure that states that inward from the surface of the Sun, the temperatures should rise dramatically. Since we are interested in the energy due to motion of these gases, we look at increase in temperatures in units of Kelvin. The hotter the interior temperatures, the more kinetic energy the particles will possess. The more energy they possess, the faster their motion and the more frequent their potential collisions. Typically, the positively charged protons repel each other, but under the unusual conditions in the core, the collision speeds are so great that these protons will stick together in spite of their like electrical charges, held together by the "strong atomic force." So much energy is released when the protons bond that a huge explosion ensues. Unlike the fission bomb made famous during the end of World War II, these fusion explosions release even greater energy. The entire process of forcing protons to stick together with the release of energy under tremendous heat is called, thermonuclear fusion. The process builds one helium nucleus from four hydrogen nuclei with the release of two gamma rays (it is far more complicated than this, and a more detailed explanation of the origin of gamma radiation can be found at Core Energy Details).

The Main Sequence Reaction Inside the Sun - The Proton-Proton Chain Reaction

The conversion of hydrogen to helium begins when two hydrogen protons fuse into one deuteron composed of a neutron and a proton, releasing a positron and neutrino. The deuteron and another proton then fuse into helium-3 (two protons and one neutron), releasing one gamma ray. Finally, two helium-3 atoms fuse, forming an atom of helium-4 (two protons and two neutrons) and releasing two protons. Since two helium-3 nuclei are fusing, two gamma rays are made for the fusion of one helium-4. The entire process is given below 4H --> He + energy:

This image to your left depicts the first step in the fusion process. These events are collectively known as the "proton-proton chain" and is considered by astronomers to be the method that all stars employ in generating light. While you might think the object of greatest interest is the formation of successively heavier elements, the very lives we enjoy are far more concerned with the formation of the positron and its fate. To learn more about the positron and neutrino, go to Core Energy Details.

 

 

 

What is not shown in this set of diagrams is what happens to the positron. When the position strikes an electron, both are annhiliated. The electron is exactly opposite it all properties from the positron, therefore the positron is considered antimatter to the electron matter. When matter and antimatter collide, they both annhiliate. The resulting annhiliation of the positron and electron produces 2 additional gamma rays.

As you might notice, the image to your left is the third stage of the proton-proton chain, and the second stage is missing. Since I think the second stage is a bit more complicated and relates to the formation of the energy types in the Sun, I have moved its discussion to Core Energy Details.

In this third stage of events, a deuterium collides with a fast-moving proton to create "light" helium. The term "light" refers to the lack of a neutron in the nucleus. Helium has two protons and two neutrons. Light helium has the defining two protons that make it helium, but only one neutron. Thus, light helium is an isotope of helium.

Additionally, the collision produces a gamma ray in the form of a high energy photon. This is the energy which we are most interested in.

In the final stage, two light helium nuclei fuse to make one helium with the release of a pair of protons. The two protons can then scurry about the solar interior to perhaps collide with each other and eventually make it to the next level in atomic synthesis. No energy is release in this final step. What is of interest here is that helium is a stable molecule in terms of further fusion events. Temperatures in the 15 million K range are insufficient to force helium nuclei to collide with fusion energies, as difficult as this might seem to our minds. Afterall, 15 million K is pretty high!

 

 

 

 

Sir Isaac Newton defined one of his laws of physics as the Conservation of Mass. This law states that mass can neither be created nor destroyed. The mass of the four hydrogen nuclei which ultimately be fused together amounts to 6.693 x 10e-27kg. The mass of the fused helium nucleus totals 6.645 x 10e-27kg. Somehow, 0.048 x 10e-27kg of mass is lost in the thermonuclear fusion process. While this mass has seemingly disappeared, Isaac Newton’s law has not been violated. Albert Einstein wrote his famous field equation which stated that mass is also related to energy and that mass and energy can be converted from one to each other according to the formula E=mc2.

0.43 x 10e-11J = (0.048 x 10e-27 kg)(3x10e8m/sec)2

How Nuclear Fusion Works in the Sun


AMU = atomic mass unit, proton=1 AMU ( 1 AMU also equals 1.67x10-27kgs)

Mass of 4 H atoms: 4x1.007825=4.03130AMU

Mass of He atom: 4.00268AMU

Difference: 0.02862AMU = 0.71% of original mass

If 4 grams (1/8 ounce) of H are converted to He, 2.8x10-3 grams are converted to energy:

E=(2.8x10-3grams)x c2 =2.8x10-6 kgs x(3x108m/sec)2

=2.6x1011 joules or enough to keep a 60-watt light bulb shining for over 100 years

This tiny amount of lost mass is converted into a relatively large amount of energy because the small mass is multiplied by the speed of light squared. When you consider the incredible mass of the sun and that 5 million tons of mass are converted into pure energy each second of the sun’s lifetime, you can now realize how the sun is able to release the tremendous energy levels discussed earlier in this unit. In fact, that change of 5 million tons of energy equates to:

3,860,000,000,000,000,000,000,000,000,000,000 ergs! This is 3.86x10e24 watts! That is a lot of energy, and to think that Earth receives only 1 two-billionth of that total, and of that meager amount, only .2% is used to power photosynthesis is extremely remarkable. And yet even this small total of energy is enough to globally construct 10e11 tons of new plant matter each year! What an amazing object the Sun is, and how important is the energy it gives.

Gamma rays are deadly, and life here on Earth would be impossible without the protection offered by the Sun's outer envelope. The gamma rays released in the core cannot penetrate that envelope. They are immediately absorbed by atoms and then re-emitted. Gradually the energy works its way through the outer layers. The inner parts of the Sun's core are 15 million K, but the Sun is cooler farther away from the core. The photons that are remitted in the outer layers must have lower energies than those emitted more interior to them. Since energy cannot be created or destroyed, there MUST be more photons to make up the difference. A single gamma ray created in the solar core will --- after nearly a million years --- result in the release of thousands of optical photons --- those seen with the eye from the solar surface.

Although solar astronomers have learned much about the sun's energy production, one puzzle remains the subject of particular focus. Scientists have determined that the conversion of hydrogen to helium yields byproducts known as neutrinos - particles of no electric charge and virtually no mass that travel out in all directions and pass through nearly everything in their path. These neutrinos pass out from the sun at the speed of light and 70,000,000,000 bombard every single square centimeter of the earth each second. Yet elaborate devices designed to detect them have found only 1/3 the number of particles predicted by the prevailing theory of solar physics. Despite a multitude of possible reasons for this so-called neutrino deficit, the case of the missing neutrinos remains open.

Please proceed to Electromagnetic Radiation or return to the Sun Introduction, or to the Syllabus.


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