A short description of the Coulomb force.

You are made of star dust.

How can that be? Because everything on Earth including you and me are made up by atoms that were produced in stars. These atoms did not form when the Universe was born some 14 billion years ago. Many of them were formed afterwards inside stars.

Stars work as a (very hot!) nuclear oven. The fuel for the oven is heat and matter such as Hydrogen and Helium, and the products that come out are atoms such as Carbon, Oxygen and a bit of sun rays. We know these atoms from our everyday life.

We are here going to explore how atoms form inside stars. More specifically, we are going to look at how the nuclear fusion is triggered, i.e. how the ‘baking process’ of Carbon starts, how the ‘baking process’ of Oxygen starts, etc. After all, the atoms are not created at the same time, even though they are created inside a star!

But first let us start somewhere else…

Nature wants you to be lazy

Imagine you live alone and you must do all chores yourself (yes, imagine…).

Bills, dishes, cleaning, laundry, lawn mowing – all of that. One day you get a bright idea: to get a room mate! It cuts the chores in half. You pay half the rent, clean half the flat, you mow half the lawn. Excellent! Only upsides to the outcome of this magnificent idea.

The moment you realize getting a room mate would result in less work for you. Illustration: Astronomicca.

Before you can enjoy the relaxation it is to look at someone else cleaning your house, you need to overcome the hurdle of finding that person. And it can not just be any person. It has to be a person who fits your requirements for a room mate.

Maybe you like to watch Netflix or maybe you play the flute. Whoever will live under the same roof as you will have to enjoy these activities as well, at least to some extent. So the search for the perfect room mate sets in and after a large effort, you find someone and dive into the efforts of moving. Packing down old books, lifting boxes, driving a van to the new home, etc. All the heavy work that none of us really want to do unless there is a prize to gain at the end.

After all the heavy lifting is done, you are now two people instead of one. Congratulations! You can now cut the energy you spend on house work in half. Excellent. More time to relax.

After overcoming the hurdle of finding a room mate, you are low left with the sweet pleasure of using less energy on work. Illustration: Astronomicca.

Things go well and you enjoy the new life with only half the chores, and so does your room mate. One day you sit together and look at the house. It is quite messy. Someone needs to clean up. And that is when it strikes you: If you are three people, you only have to do 1/3 of the chores. That is even less than half. Once again: Excellent.

But now you are two people to decide which qualities you want in a room mate and once again a moving-day needs to be organized. Once again, it is a hurdle and this time the hurdle might seem even bigger because two of you have requirements. But – if you overcome the hurdle, you will in the end minimize your energy and have a more lazy efficient life.

You might see a pattern here. Each person can minimize energy by ‘fusing’ with another person. But before the fusion can happen, a hurdle needs to be to overcome. This process only works until a certain amount. Imagine you live 30 people in a single flat. Then you might end up spending more energy being around these people, than you would if they left.

This point is crucial, so please read it a few times as it will give a Eureka!-moment later.

A visualization of how you can optimize laziness by getting room mates, i.e. release the energy you would normally spend on chores. It only works until you reach a limit where the high number of people start to drain you. After that your house becomes unstable. Atoms work the same way. Illustration: Astronomicca.

The description above fits exactly on how atoms form via nuclear fusion inside stars. But before we can dive into nuclear fusion, let us first look at the atoms in the Universe.

Fusion in the center of a star

The lightest atoms in the Universe are Hydrogen and Helium. They were made when the Universe was created billions of years ago. Since then, more atoms were created such as Carbon, Oxygen, Nitrogen and all the heavier elements that are needed to form you and me.

Some atoms are made inside stars during their life-time and some are made when stars die. In this post we will only be looking at the atoms that form inside stars during their life.

Let us dive in..

The fusion of atoms happens inside the central core of a star. Atoms up to Iron are formed inside stars. When astronomers say “up to Iron” they refer to the order of elements in the periodic table, which is shown below.

Periodic table of elements. Elements up to Iron (called Fe, no. 26, on row 4, column 8) are created inside the center of stars. The number refers to the amount of protons in the nucleus of the atom. Iron has 26 protons in the nucleus. The other row/column-numbers and box-colors are irrelevant in this context. Illustration: Wiki Commons.

Just like the room mate analogy, the fusion process starts when one proton wants to save energy (because it is practically as lazy as us), and it can do this by fusing with another proton. This is how two Hydrogen nuclei, which are just two individual protons, form Helium. Helium is an element with two combined protons.

(The real world is of course a bit more complicated than this. Helium also has two neutrons. So in reality 4 protons are needed, where two of them are converted into neutrons and two stay protons. But forget about neutrons for now.)

The fusion process does not happen immediately. Why? Because there is a (yes, you guessed it) hurdle to overcome. That hurdle is called the Coulomb force and we will get back to that shortly. Later on, Helium nuclei start to fuse with other Helium nuclei to form even heavier elements such as Carbon and Oxygen. But, again, only once they overcome a hurdle, that is even bigger than the previous one, which Hydrogen encountered.

This goes on all the way up until the formation of Iron (which has 26 protons in the nucleus) in the center of the star. The atomic hurdles, i.e. the Coulomb forces, are overcome in the center of the star, when the temperature is high enough.

All new nuclear fusions are triggered in the very center of the star and not, say, in the outer layers of the star. Each time a new fusion is triggered, the rest of the atoms “are pushed” out in the shell. The Coulomb force is therefore only overcome in the very center of the star.

Fusion of new, heavier atoms is triggered in the center of the star. Illustration: Wiki Commons with edited text.

The Coulomb Force

In the beginning of the star’s life the temperature in the central star is around 15 million degrees Celsius. At this temperature Hydrogen (1 proton) fuses to Helium (2 protons) and the process emits energy that we see as sun rays. The temperature of 15 million degrees Celsius is crucial as this is what the Hydrogen nuclei need to get enough energy to overcome the hurdle that is the Coulomb force.

The fusion process causes a core of Helium to slowly build up in the center while at the same time creating an increase in the star’s central temperature. Around this Helium lies still the Hydrogen atoms, that continuously fuse into Helium. At some point Helium will start to fuse into Carbon. This happens if the central core of Helium reaches 200 million degrees Celsius.

Why are these high temperatures needed before the heavier atoms can start to fuse? Why do all atoms not just burn at the same time?

Good question (thanks!). The reason is found in the so-called Coulomb force. This force acts as a barrier which atoms need to overcome before they can start to fuse. Like a person looking for a room mate, there are hurdles to overcome because laziness largely defines us. For the atoms that hurdle can be overcome by a high enough temperature. The larger elements we want to form via fusion (e.g. Carbon or Oxygen), the higher temperature we need to overcome the hurdle that is the Coulomb force.

Atoms like humans do not like to overcome hurdles unless there is something to gain on the other side. Each particle in the atomic nucleus likes to stay as lazy as possible.

So, if we look at a graph showing how much energy an atomic nuclear particle can save by fusing into a higher element, it will look something like this. Note, that we now look at the energy of individual particles in the nucleus of the atom.

Atoms can save energy (mass and energy are the same) by fusing into heavier elements – but this only works up until Iron. After that the atoms become unstable. Illustration: Wiki Commons.

Looks similar to The Laziness Graph above, doesn’t it? It shows how much energy the particles can save if they juuuuuust overcome the hurdle that is the Coulomb force so they can merge into a heavier element. But this is only possible up until a certain point – just like in the case with getting too many room mates.

After this point (defined by Iron with 26 protons) atoms start to become unstable as there are too many particles in the nucleus. Therefore it is no longer energy efficient for atoms to fuse into heavier elements once they go beyond Iron. That is why elements heavier than Iron can not form inside the core of a star.

Now you might wonder: So where DO all these heavier-than-Iron elements form? How does gold form? How does silver form? They form in supernova explosions. But we will leave that topic for another day.