November 11th 2016

Atoms are mostly empty space, so why doesn’t the world collapse and then blow up?

Atoms make up all of the matter in our universe and they are amazingly tiny- you can line up 200,000 of them along the point of a pin. Atoms are composed of positively charged protons, neutral neutrons, and negatively charged electrons. The protons and neutrons make up the nucleus of the atom and the electrons reside in electron clouds around the atom.

Atoms are Incredibly Tiny- an Overview of Length Scales

Despite how small atoms are, the components that make them up, are many times smaller. The nucleus of a hydrogen atom, for example, is almost 300,000 times smaller than the width of the electron cloud around it. If a hydrogen atom was the size of a football field, its nucleus would be the size of a pea! This means that atoms are mostly empty space. So why does matter feel so solid? Why can’t I push my hand through a table or fall through the floor?

The Ratio of a Nucleus to its Electron Cloud is the same as a Pea to a Soccer Stadium

We will tackle the reason why we can’t push atoms through each other over the next few blog posts. The answer ultimately lies in quantum mechanics, and let’s first set the stage for why all of this empty space is critical for explaining the world that we live in.

Electrostatics- what electrons have to do with static electricity

Positive and negative charges attract each other due to a Coulomb Force that gets stronger as the objects get closer together. You’ve experienced this if you’ve ever rubbed a balloon in your hair. Rubbing the balloon will add a few electrons to make it negatively charged. If we rub a glass rod with silk, that will strip off several electrons which leaves the rod positively charged. The two objects will then experience an attractive charge toward each other- i.e. opposites attract. See this video by Bill Nye that shows this in action:

The attractive force goes as 1/r2 , where r is the distance between the two objects. As r gets tiny, the force gets enormous- in fact at 0 distance, the two charges will have a force that is infinitely large. This attractive force should exist between a positively charged nucleus and a negatively charged electron, but if this was true we’d expect the electron to spiral into the nucleus until the distance became 0, which would make it impossible to separate the two. So why exactly don’t all of the atoms in the world collapse in on themselves? We will show that quantum mechanics prevents opposite charges from ever getting close enough to create these pesky infinities.

Conservation of energy- energy can change from potential to kinetic but cannot be destroyed

It turns out that the story is even worse if you look at what would happen to the energy of such a system. Energy can never be created or destroyed, but its type can be changed. For example, we can roll a rock up hill and convert kinetic energy of pushing it up into potential energy. In the opposite case, if our system goes to a more stable state that has less potential energy, it will have to give up that difference in energy as kinetic energy, such as through heat.

Let’s say we had two glasses of water and combine them into one container. The number of possible interactions for an oxygen atom in the water will double because there is now twice as much water.

The force of attraction between the protons and electrons will grow with the number of particles squared. This means that the attractive force of mixing the two water glasses is not simply the mixture of the two, but it will go as the number of particles times itself. This is similar to the difference between 2×10=20 versus 102=100- squaring the number will give you a significantly higher number than simply doubling it. When you are considering numbers of charges that is on the order of 1023, such a situation can quickly get out of control and it would suggest a huge release of energy when matter is added together.

In fact, the amount of energy liberated from simply mixing two beakers of water would be as much as 100 million nuclear bombs! Can you imagine living in fear that your neighbor could blow up the planet simply by pouring milk over her morning cereal?

Conclusion: Uncertainty in Quantum Mechanics is needed to keep matter stable

Luckily for your neighbor Rose and her proclivity for morning cereal munching, a force exists that tamps down this coulomb force and keeps it under control. The result is that if you have a beaker of water and combine it with a second beaker, the amount of energy in the combined system is just the sum of the two things you combined instead of the square of that. This fits with how we experience reality- the energy released from burning two logs is just twice as big as burning one, for example.

The solution to this problem was ultimately solved by physicists at the turn of the twentieth century by developing a new branch of physics called quantum mechanics. A core tenant is that we cannot know both the position and momentum of small objects such as electrons. It turns out that this uncertainty in the position of the electron prevents it from being confined enough to maintain the volume of the atom.

Check out our next post which will show how quantum mechanics solves this potential catastrophe.