 Each second the Sun produces 3.8 into 10 to the power 26 joules of energy. In this video we will see that the Sun is not nearly hot enough to be able to produce this much energy. It is too cold, so cold that it shouldn't be alive. Let's see why. Now as we speak protons are smashing into each other in the Sun's core, releasing a huge amount of energy. This kind of reaction is called a nuclear fusion. Just like as if we had two water balloons approaching each other with some velocity, colliding and in doing so releasing the water inside. In nuclear fusion we can think of energy released as water over here. But we know that the two protons will repel each other because they have the same charge. They are both positively charged. So how can protons come close enough so that they fuse to release all this energy? We can take some hint from this analogy. Only if the balloons are approaching each other with sufficient velocity, they will burst open to release all that water. Similarly the protons must have sufficiently high velocity to begin with. Only then they can overcome the Coulomb repulsive force and fuse. For high velocities we would need high temperatures. The temperature of the core of the Sun must be high enough. This can be expressed mathematically. We can write that the average K of all the particles in the Sun's core it is proportional to the temperature. And when we remove the proportionality we get 3 by 2 into the Boltzmann constant Kb into the temperature. This is the average kinetic energy of the protons in the Sun's core. It is directly related to the temperature of the core. And value of this Boltzmann constant that is 1.38 into 10 to the power minus 23 joules per Kelvin. We are interested in the temperature of the Sun's core so let's keep temperature on one side and bring everything else on the other side. So this is what our equation becomes. If we know the kinetic energy of the protons then we can figure out the temperature right. Now protons they repel each other as they come close their velocity must decrease which decreases their kinetic energy as well. At this point why don't you pause the video and think about where is this kinetic energy going? Is it transforming into something? Is it not? Why don't you pause the video and give it a thought. Alright naturally if protons are just left to themselves they would never want to approach each other but when they are made to approach each other because of in this case because of high velocity their potential energy must increase. So kinetic energy in this case is being transformed into the potential energy of the two protons and according to conservation of energy principle according to conservation of energy principle we can write that the total mechanical energy initially when the protons were far apart that is equal to the total mechanical energy finally when the protons are close enough to fuse. We can expand this and write it in this manner the total mechanical energy and initially and the total mechanical energy final. Here u is the potential energy initial and final. Now initially we can assume that the protons are far apart and they are not interacting with each other in any way. So the initial ui the initial electrostatic potential energy is zero considering that the protons are far apart and there is no interaction whatsoever and final kinetic energy that is also zero because when protons are close enough so close that they can fuse they have lost all their velocity and they are about to go back but they can't because they have come so close that they end up getting fused. So final k is also zero and initial potential energy is zero. That gives us the initial kinetic energy of both the protons that is equal to the potential energy the electrostatic potential energy of the two protons. Now let's try to work this out and figure out the kinetic energy. So this is this is equal to the final potential energy that is 1 by 4 pi epsilon 0 into the charges that is q1 q2 divided by the distance between the center of the two protons. Now this is equal to 1 by 4 pi epsilon 0 and instead of this huge constant we can write 9 into 10 to the power 9 into q1 q2 both of them are protons so both of them are positively charged and they have the same charge and that is 1.6 into 10 to the power minus 19 whole square because you have q1 q2 here divided by r the distance between the centers which should be 10 to the power minus 15 meters or 1 femtometer. Only if the protons are this close they will be able to fuse and release energy. We can work this out or we can just directly multiply this fit 2 by 3 into kb that will give us the temperature the temperature of the sunscore. So multiplying this further with 2 by 3 kb will give us the temperature the final temperature of the sunscore and i encourage you to pause the video and try out this entire calculation on your own. All right hopefully you have given this a try the temperature that you should have arrived at is 1.1 into 10 to the power 10 kelvins but now the real temperature of the sunscore is not this it is much lower it is 15 into 10 to the power 6 kelvins or 15 million kelvins it is much lower than what we arrived at. This temperature will not give enough velocity to the protons so that they can come closer and fuse and that is why the sun should not be alive but of course it is alive. How can that be? What is happening here? It turns out that classical physics that is thermodynamics or newton's laws conservation of energy they won't be able to explain all of this but quantum physics does explain why the sun is alive and it is particularly it is quantum tunneling effect which makes it possible for the protons to fuse even at a temperature of 15 million kelvins. Now we will not be going into how exactly quantum tunneling helps but the amazing thing is that just sitting on a chair with a piece of paper and some knowledge of electrostatic potential energy and conservation of energy we were able to predict the temperature of the sunscore and form a really sound argument on why the sun shouldn't be alive.