hello everyone this video is on the production of energy in stars by way of review einstein's mass energy equivalence principle is important to understand before we delve into the details of how stars produce the energy einstein proposed that energy and mass are interchangeable as governed by his famous equation e equals m c squared whereby energy can be transformed into mass and vice versa this principle also obeys the laws of conservation of energy and mass that is the combined energy and mass before a particular reaction should be equal to the final energy and mass when using this equation there are numerous units we can use when mass is embedded in kilograms we'll be calculating energy in joules when mass is in atomic mass units we'll be calculating the energy in mega electron volts or mbv stars produce energy via process called nuclear fusion this is when small nuclei of elements will fuse together to produce a larger nucleus during nuclear fusion a small amount of mass will be transformed and converted into energy as we'll see in a moment main sequence stars like our sun produce energy via two types of nuclear fusion reactions the proton proton chain ppc for shorts and the carbon nitrogen and oxygen cycle the c and o cycle for shorts in a proton proton chain the word proton refers to a hydrogen one nucleus this is because in a hydrogen atom the nucleus only contains a single proton so when the electrons are not present the hydrogen atom becomes simply a single proton the proton proton chain involves numerous steps with each step involving the addition of protons in the first step two protons undergo nuclear fusion to produce a hydrogen two nucleus it's hydrogen two in this case because now there is a single proton as well as a neutron in a nucleus the number two here is the atomic mass number which denotes the number of protons and neutrons combined together in the nucleus during this first step nuclear fusion a single proton has been converted into a neutron the hydrogen ii nucleus then undergoes another round of nuclear fusion with an additional proton to form a helium-3 nucleus when the proton number changes the identity of the element also changes this is why the product here becomes helium and is no longer hydrogen and again it's helium 3 because there are total of three protons plus neutrons in a nucleus when we get two of such helium-3 nuclei they will then fuse again together to give us the final product of the proton proton chain that is a helium-4 nucleus during this nuclear fusion we also produce two additional protons which are not included in the helium-4 nucleus the final product here remains to be helium because the number of protons is still two but we call this helium four because there are four protons and neutrons in the nucleus so essentially as an overview of the proton proton chain what we've done is we've combined together four protons at the beginning two protons in the second step which add to a total of six protons to produce a helium four nucleus and two protons since we are producing two protons the net amount of protons that are actually converted and fused to form the helium-4 nucleus are four protons if we consider the approximate mass of a single proton of 1.008 atomic mass units four protons will give us a mass of 4.032 atomic mass units however the mass of one helium nucleus is approximately 4.003 atomic mass units you can see that the mass of four protons is slightly greater than the mass of a helium-4 nucleus this difference in mass has been transformed into energy and this is the energy produced by the proton proton chain we can actually use einstein's mass energy equivalence equation to calculate or to estimate the amount of energy produced every time a helium 4 nucleus is produced we can convert this mass difference into kilograms by multiplying 1.661 times 10 to the power minus 27 and then multiplying by the speed of light in meters per second squared and this will give us 4.34 times 10 to minus 12 joules for every helium 4 nucleus formed we can also leave the mass difference in atomic mass units and multiplying this by 931.5 to give us the same amount of energy but in mega electron volts so every time a helium-4 nucleus is formed from the proton proton chain we can expect there to be 27 mega electron volt of energy produced this isn't very much but you need to imagine that in stars like our sun there's a vast quantity of helium four nucleus being formed from this type of nuclear fusion although each time nuclear fusion occurs only a small amount of energy is produced as a total stars are able to produce a much larger quantity of energy in a sustainable manner the carbon nitrogen oxygen cycle or the cnn cycle is another type of nuclear fusion that we see in main sequence stars as the name suggests this nuclear fusion involves a cycle of reactions between isotopes of carbon nitrogen and oxygen as you can see this nuclear fusion is much more complex than the proton proton chain the details are not important what you should focus on is that at different points to the cycle four protons have been incorporated to help transform between the different elements at the end of the cno cycle the four protons i've incorporated will lead to the formation of a helium-4 nucleus this is exactly the same as what we saw in the proton-proton chain four protons will join the cycle to produce a helium-4 nucleus and as i discussed earlier for the proton proton chain this is one way of how nuclear fusion is able to convert mass into energy so every time one c and no cycle occurs a small amount of energy has been transformed from the mass difference between four protons and the helium for nucleus main sequence does use the proton proton chain and the cno cycle to produce energy however main sequence stars vary greatly in terms of the luminosity and the mass heavier stars that is the ones with higher luminosity or rate of energy production tend to have a higher core temperature on the herdspawn russell diagram main sequence stars that light on the top left part of the diagram tend to have heavier mass and higher luminosity main sequence stars that lie on the bottom right side of the diagram have lighter mass and lower luminosity this is important to know because depending on the mass and luminosity main sequence stars will utilize the proton proton chain and the cno cycle to different extents energy produced from lighter main sequence stars tend to be derived from the proton proton chain more so compared to the cno cycle vice versa energy produced in heavier main sequence stars tend to be derived from the cno cycle more than the proton proton chain as an example up to 98 of energy produced by our sun is due to the proton proton chain only the remaining two percent will be derived from the cno cycle now why does the mass or the temperature of the star's core make such a big difference in what type of nuclear fusion it uses this is because higher temperature in the core will overcome the electrostatic repulsion between heavier nuclei the cno cycle involves carbon nitrogen and oxygen which are heavier nuclei compared to the protons and helium nuclei that we saw in the proton proton chain when the nucleus has more protons it has a greater positive charge so there will be a greater amount of electrostatic repulsion between nuclei with more protons in them when the star's core has a lower temperature these nuclei are less likely to collide and fuse with one another due to this greater repulsion this is why when stars have a higher temperature the additional amount of energy given to the nuclei will help them overcome the repulsion between the heavier nuclear with more protons this graph can help us understand the effect of temperature of the star's core on the extent to which they utilize the proton proton chain and a cno cycle lighter stars that have a lower core temperature more energy is derived from the proton proton chain but at a certain temperature main sequence stars will start to produce energy more so from the cno cycle compared to the proton proton chain it is also important to know that the cno cycle produces energy more efficiently compared to the ppc the proton proton chain or ppc is proportional to the temperature of the star's core to the power 4 whereas the cno cycle is proportional to the temperature to the power of 17. the triple alpha process is another nuclear fusion reaction that occurs in post main sequence stars that is the evolutionary stage of stars after main sequence stars the triple alpha process utilizes helium nuclei that were produced from the proton proton chain and the cno cycle to produce heavier element or heavier nuclei the reason why this nuclear reaction is called the triple alpha process is because it involves the fusion of helium nuclei at three different stages of the reaction a helium-4 nucleus is also known as an alpha particle initially two alpha particles undergo nuclear fusion to form a beryllium eight nucleus then this beryllium nucleus fuses with another alpha particle to form a carbon-12 nucleus this carbon-12 nucleus further fuses with another alpha particle to form an oxygen-16 nucleus as you can see in the triple alpha process alpha particles have been incorporated in a nuclear fusion are one two three parts of the reaction the triple alpha process is only present in post main sequence stars such as red giants because the higher core temperature of post main sequence stars will provide enough energy to overcome the natural electrostatic repulsion between the protons in these larger nuclei the fusion between beryllium and alpha particles or carbon and alpha particles could not have occurred in main sequence stars because there was not enough energy in the core of those stars to overcome the electrostatic repulsion between these elements the power of the star in other words the rate of energy production is heavily associated with the mass of the star as the mass of the star increases the gravitational force exerted on the outer layers of the star also increases the gravitational force will cause the star to contract and eventually collapse to prevent the collapse the star needs to produce energy to overcome the gravitational force the energy produced by nuclear fusion will radiate outward and the pressure exerted by this radiation will balance the gravitational force exerted on the outer layer of the star preventing its collapse so the shape of the star is really the result between the outward force produced by fusion and the inward force produced by gravity thus for a heavier star it needs to produce more energy at a greater rate to overcome its much larger gravitational force this is the reason why heavier stars will have a greater luminosity which is related to the power or the rate of energy production and a negative magnitude which is the brightness of the star more negative the magnitude the brighter the star due to the much higher rate of energy production heavier stars also burn through their mass faster resulting in a shorter lifespan remember that the way stars produce energy is through the mass energy equivalence principle by transforming the mass in the form of nuclei into energy if the rate of energy production is higher then the rate of this conversion is also higher when the star runs out of mass to transform into energy then that will be the end of its lifespan so heavier stars require greater power which results in a shorter lifespan this concludes the video on energy production of stars