How can we explain why electrons don't spiral into the attracting nucleus?

2 Answers
Jul 17, 2017


That is the "energy" of the electron. There is no opposing force.


Essentially, at the atomic scale, the electron is orbiting in a vacuum. With no "drag" there is nothing to reduce its angular momentum around the nucleus.

Jul 17, 2017


Here's how I would explain it.


This is exactly what classical physics predicts.

However, we now know that electrons are governed by the laws of quantum mechanics.

Electrons don't really orbit a nucleus.

Instead, we must think of the electron as a cloud of electron density.

The electron could be anywhere in a spherical "shell" around the nucleus.

We could think of the atom as consisting of many thin shells with radius #r# and thickness #Δr# arranged like the rings of an onion, as in (a) below.

Radial distribution
(From Chemistry LibreTexts)

For each shell, the area is #A = 4πr^2# and the volume is #V = 4πr^2Δr#.

The probability density is greatest at #r = 0# [as in (b) above].

As we move outwards, the area #A# and the volume #V# increase as in graph (c) above.

However, at large distances from the nucleus, the probability density is quite small, so the probability #P# is near zero [graph (b) above].

Also, close to the nucleus, the volume of each shell is small, so the probability #P# is near zero.

So, the highest probability of finding the electron is going to be where the volume of the shell is big enough that #P# is high, but the distance from the nucleus isn't too large for #P#to be low.

Thus, a plot of radial probability has a maximum at a certain distance from the nucleus [graph (d) above].

Most important, the probability of finding an electron at the nucleus is zero.