The core of the sun is extremely hot, about 15 million degree celsius. But it is not hot enough for nuclear fusion to take place. For nuclear fusion reaction to take place, you need a temperature of at least 100 million degrees. If the sun’s temperature is not hot enough, how does nuclear fusion take place?
I mean, if nuclear fusion does not occur in the sun, then it won’t be a star. Stars are called stars because nuclear fusion takes place inside them. Nuclear fusion is when two or more protons fuse together to form a heavier element. For the sun, it’s two hydrogen fusing to form helium. When we say hydrogen or helium, we mean only the protons contained in them. The electrons of the atoms are all ready knocking off by the extreme heat and pressure. The combined mass of the protons before fusion is more than the combined mass after fusion, so the lost mass is converted into energy. It releases about 26.7 MeV of energy for every nuclear fusion reaction that fuses hydrogen into helium.
Now, quantum tunnelling is like you are standing on one side at the foot of a hill. To reach the other side of the foot of the hill, you have to climb the hill and then climb down again to reach the other side. And for that, you need energy. But, in quantum tunnelling, you stand on one side of the foot of the hill, but you don’t have enough energy to climb up and reach the other side. Somehow, you mysteriously appear on the other side. It’s like you passed through a tunnel connecting the two foots of the hills.
You might be wondering why we don’t see in real life. The answer is here, for just one proton or electron to quantum tunnel, it has a probability of one proton/electron quantum tunnelling out of 10^28 protons i.e. 1 in 28 protons quantum tunnel. And the chance is 10^-28 for just one proton to quantum tunnel. The chance is extremely low, almost negligible. Again, you are made of at least 7*10^27 of protons, so the chance of 7*10^27 protons quantum tunnelling at the same time is extremely low about 10^-55, which is ridiculously low. That’s the reason why we don’t see quantum tunnelling in normal day-to-day life activities.
But at the core of the sun, things are different. The main component in the sun is hydrogen. In the sun, when we say hydrogen, it’s the proton because the electrons are knocking off due to extreme pressure and high temperature. In the sun’s core, there are about 10^56 protons moving here and there. To make them bump into each other, we need to quantum tunnel as they don’t have enough energy to bump into each other. The reason why they require so much energy to bump into each other is that when same charges like protons stay close together, the electromagnetism become exponentially stronger. And it repels two protons with a force of 20N. With such force on subatomic particles, the protons would attain speed of more than 8000 km/sec.
But if we could just make them close enough about 1 femtometer (10^-15m) apart between two protons, the strong nuclear force would overcome them and they would form a heavier nuclei. Now for the quantum tunnelling part. Remember we said that there is a chance of 1 in 28 protons to quantum tunnel and there are about 10^56 in the sun’s core. So, about 10^37 nuclear reactions occur in the sun every second, which is a huge number. Again, each fusion reaction gives out 26.7 MeV of energy. And there are 10^37 reactions every second. So, you calculate out. And there you have it, the amount of energy released by the sun per second.
One last question might still be there in your mind, if quantum tunnelling can make fusion reaction work, why can’t we use it on Earth to make fusion reaction work? Well, it’s because there are not enough particles to quantum tunnel on Earth. The chance of a proton quantum tunnelling is 10^-28, so large amount of protons are required to fuse proton regularly. But on Earth, there’s just not enough particles to make this happen. So, that’s the reason.
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