# What is in the space between a nucleus of an atom and its electrons?

There is a common analogy about the structure of an atom, such as the nucleus is a fly in the centre of a sports stadium and the electrons are tiny tiny gnats circling the stadium (tip of the hat to 'The Greatest Show on Earth') but what is in the space between the 'fly' and circling 'gnats'?

Short answer: The space between the nucleus and the electron is not empty space, it is filled with an electron cloud. (You will understand this answer better if you read the long answer)

Long answer: Firstly, physics is a description of what we can observe. Depending on the scale of which you are describing, physicists, over the years, have different mathematical descriptions describing at different scales.

When you ask about the space between the electron and the nucleus, confusion arises when trying to use a classical description to describe things on the atomic scale.

On the atomic scale, physicists have found that quantum mechanics describes things very well on that scale. And when we use quantum mechanics to describe particles, electrons, protons, neutrons, etc, they are no longer thought of as point like particles whizzing around like the description that you are confused about.

Particle locations in quantum mechanics are not at an exact position, they are described by a probability density function. The previous answers other people gave before me are links to pictures of a probability density function of Hydrogen at different energy levels in 3D space.

These probability density function's shapes are often known as "electron clouds". They show where it's likely to find the electron. The darker regions are places of higher probability of finding the electron and the lighter regions are lower probability of finding the electron.

An important thing to note is that the pictures show "white space". Its actually a smooth picture with the probability getting smaller and smaller so fast that those locations look "white". This means that the probability of finding the electron in those seemingly white spaces are extremely low.

Now what does it mean to "find and electron?" This is another question you will have to ask. Its not related to this question.

• I swear electrons are limited to only certain areas, at all. Because you can only have electrons at certain energy levels. So electrons are only "allowed" at specific distances from the nucleus? – Jonathan. Nov 26 '11 at 9:12
• Chris Gerig, you've got to keep in mind the person who asked the question. Yeah, sure its filled with virtual particles. But the original person who asked the question is gonna get confused by this. Unless you now explain virtual particles too. Please do! So that it adds more depth to the answer. – QEntanglement Dec 21 '12 at 2:00
• Also, the person who's asking the question is mentally transitioning between the classical picture to the quantum one. It wouldn't help to blast a whole Tsunami of information in their face. – QEntanglement Dec 21 '12 at 2:02
• I would like to add that for S state orbitals, S being the zero angular momentum orbit, the solution goes right through the nucleus, so the electron probability certainly fills the inside spaces, which is how we can have capture nuclear reactions. – anna v Dec 21 '12 at 5:35
• @RhysW No. You're trying to work from the Bohr picture which is horribly incomplete. You need to solve the 3d Schrödinger equation. The "orbitals" are not orbits and are instead space filling three-dimensional functions (albeit with regions of zero probability called nodes). For high angular momentum states there are some of these functions which begin to approximate a fuzzy orbit, but those are the exception. The lowest lying states are spherically symmetric and strongest at the center fading outward. – dmckee Jan 30 '13 at 6:07

Maybe one should add to the analysis of @QEntanglement and the nice electron probability clouds in the illustrations in the other answers, that also the space between the nucleus and the electrons is teaming with the exchange of virtual particles between the electrons and the nucleus, necessary to create the potential which determines the energy levels of the particles. These will mostly be virtual photons with loops and stuff.

• Anna V. I agree with you. Perhaps Chris Gerig can do this for us. He seems very passionate about how my answer is wrong. – QEntanglement Dec 21 '12 at 1:59