No Quantum Tunneling, No Sun?
Since grade 8, you must have been told that “Sun doesn’t burn but rather produces its energy by converting hydrogen into helium in its core through a process called Nuclear Fusion”. Now, it is not false but not completely true either. When you further investigate the process, you realize that to achieve nuclear fusion it requires approx 100 million degree Celsius (or 100 mil kelvin). Well, ideally it does need that much temperature. But what if someone came and told you another fact: The Sun’s core has a temperature of approx 15 million degree Celsius. What???? Something does not fit the picture very well. If the Sun’s core temperature is so less than what is needed to bond protons together to make nuclear fusion possible, then what the ‘hell’ is happening inside the Sun!
The answer is Quantum Tunneling and no I am not Nolan-ing you out.
To understand Quantum Tunneling, we need to add a little bit of knowledge to our grade 10 physics. Remember Total internal reflection, when a light beam is passing through a denser medium to a rarer (less dense) medium, the beam refracts. And then if you keep increasing the angle of incidence there comes a point where no light is transmitted and with a slight further increase in angle the beam completely gets reflected back into the same medium, the critical angle.
Hmmm, we need to add a little bit of extra information here.
When we say that after the critical angle, the beam gets totally internally reflected and no light passes through, we overlook a very very small part of the beam that does get transmitted! Yes! This part of the beam does get across the border into the next medium but dies off exponentially and hence we are just used to ignoring this tiny tail. This is called the evanescent wave. Keep this term in mind simply as some kind of a property that the wave exhibits when bouncing off a surface.
Now we come to Quantum world! Yeah! It is generally believed that very small particles like photons, electrons etc behave like both, a particle, and a wave. And now this wave is not exactly the ‘wave’ we know of. It is a probabilistic wave. Let us look at this with help of an example:
Particle in a box — A very widely used example to understand the wave nature and the quantum behavior of the particle.
Consider that there in an empty box, a particle is let free but is restricted to move in only one dimension. Now this particle can be anywhere on the straight line. But at this scale we cannot exactly point out where the particle will be at some given time due to something called the Uncertainty Principle. There is one genius escape out of this!
You go point by point to find out what are the chances of finding that particle is on that particular point. You take in all the probabilities for all these points and map it out in the form of a wave. It is this wave that physicists always talk about in quantum mechanics!
Do you realize already where we are going? Remember when we talked about a wave bouncing off a surface, there is an evanescent wave. So, if the barrier is of a small width, the small tail can go across the barrier and be present on the other side too. The wave is nothing but a way of telling the probability of finding the particle there. So, even if only a very small part of the wave is crossing the barrier, it means there is some probability of finding the particle on the other side! That is outside the box. Putting it in simpler terms, even if the particle is completely enclosed in a box, there is some (however small it may be) probability that we can find that particle outside the box as well. In scientific jargon, this is called Quantum Tunneling.
All the time we were talking about the ‘box’, it is actually a potential barrier. No need to be afraid of the term.
Coming back to the Nuclear Fusion question. There are two major types of fusion cycles in stars. In lighter stars (like our sun) we have something called proton-proton (P-P) cycle and in heavier stars something called CNO cycle but that is not important right now. We will focus on the PP cycle. Like the name suggests it involves fusion of two protons. Now, the hydrogen atom does not directly get converted to helium. Hydrogen gets converted to its unstable isotopes first and then after a long chain of reactions it settles to form helium (and several other by-products). This is fusion. It is very difficult to bring two similar charges together and bond them over. But our understanding of quantum mechanics helps us overcome the confusion. Consider one proton to be a tiny probabilistic wave, bounded in a potential barrier. We know there is always a tiny tail of this wave that pokes through the barrier and hangs out. Thus, it is of immense ease for the proton to bond with another one through this tiny part sticking out. This is the reason why the reaction is possible in the Sun’s core, even though the temperature there is far lower than what is ideally needed.
We need to keep in mind that the probability of quantum tunneling occurring is in the order of 1 in 10²⁸. But there are so many particles present in the Sun, that this reaction occurs on a very large scale and helps in fueling the entire star. Sun’s strong gravity pulls in these particles tight and thus creates favorable conditions for fusion to occur.
So, this is it!!! We are done!! But do remember Quantum tunneling is very essential for the Sun to shine and for life to exist on Earth. Nolan-ed enough!!
