Question #2 What is in the space between the electron and the nucleus?

This question comes from Paul on Facebook.

The first thing is a little about the anatomy of an atom. The nucleus of an atom is made up of protons, with a positive charge, and neutrons which have no charge or are called neutral. Around the nucleus is the electron orbits or cloud. The negatively charged electrons are considered to be in a cloud because they are moving too fast to really be able to determine exactly where they are at an given time. The electron cloud is the area around the nucleus where we expect to find the electrons.

The distance Paul is looking for has a name, the Bohr radius. Named for the famed physicist Neils Bohr this radius is the distance between a proton and an electron in an atom or the distance between the nucleus and the electron. This distance is accepted as 5.2917721092(17)×10⁻¹¹ m or 0.53 angstroms according to Bohr's work.

If you'd like to get into the math of how to figure out where an electron is based on Bohr's model this is the equation:

where:
a0 is the distance from nucleus to electron
is the reduced Planck's Constant or Dirac Constant = 6.58211928 x 10^-16 eV*s
is the resting mass of an electron
is the elementary charge or -1.602176565 x 10^-19 C


Modern Quantum Mechanics gives a different value that is approximately 1.5 times Bohr's given distance. The difference in these values is due to how classical (Bohr's) model of an electron differs from how Quantum Mechanics sees the electron. Bohr's model is what people are used to seeing where the electron is some dot on an orbit around the nucleus of the atom. Bohr's model gives it an exact point and that can be measured precisely. Quantum mechanics on the other hand measures the probability of an electron to be at any point within an electron shell. (think of an orbit that is 3D where the electron can go forward, back, left, right, up and down with in a given area. this is the shell) Due to the 3D and probability qualities of the quantum measurements the values are different. As we work with larger and larger atoms the difference between the Bohr and Quantum numbers do fluctuate.

The equation for the quantum model is much more complicated. Part of this complication is due to particle wave theory which I am not going to explain in depth here. However, basically, it is the idea that a particle (electron in this case) can move both like a particle and like a wave.

ψ = ψ(x, t) is the wave function for the electron

x and t are the space and time coordinates

m is the rest mass of the electron

p is the momentum from Schrödinger theory

c is the speed of light

ħ is the reduced Planck constant

All the other variables come from quantum matrices which we are also not going to go in depth with at the moment. You can read a little more about how this quantum model is derived here.

The pictures below will help you understand the reasons why there is the difference between the Bohr and Quantum models and equations.

Bohr's model of a nucleus with electrons orbiting.
2 orbitals are shown as the rings.

Quantum model of the possible locations of electrons at any given moment.
2 shells of electrons are shown one in grey and one in red.

I hope that has answered your question Paul.