Understanding Electron Orbits: A Physics Problem Explained

[bobsmith76]

Here is a problem from a physics text

An electron (mass 9.11 × 10−31 kg) orbits a hydrogen nucleus at a radius of 5.3 × 10−11 m at a speed of 2.2 × 106 m/s. Find the centripetal force acting on the electron. What type of force supplies the centripetal force?

I'm not interested in the answer, rather I thought that electrons didn't orbit in a Newtonian, viz, predictable fashion. I thought they sort of flew around in their orbits in a manner that only vaguely resembles planetary motion.

 

[Simon Bridge]

There are several models for atoms in physics.
Your textbook is asking you to use one of them.
As students study, they will be asked to learn about simple models before they learn about the complicated ones. The simple ones will usually be historically important, like the planetary model of the atom. They don't have to be true.

You will also find textbooks asking you to do problems in Newtonian mechanics even though we know that they are wrong too... what's the problem?

 

[EmpaDoc]

Well, one can elaborate on this.

When you are asked to calculate the trajectory of a cannon ball in Newtonian mechanics, you know that the theory is applicable - in the sense that the answer is going to be accurate to within a certain number of decimals. However, for electrons orbiting nuclei, common wisdom is that Newtonian mechanics cannot even predict many qualitative features.

On the third hand, Newtonian physics should be OK for the specific quantity asked for here - the mean force on the electron. I think we are really applying Ehrenfest's theorem here (saying that by taking expectation values, an equation in the form of Newton's second law can be derived from the Schrödinger equation).

 

[sophiecentaur]

You've been asked to take a historical trip into the birth-time of Modern Physics. People were trying to get answers from calculations like the one you have been given - then they had to invent QM and beyond.

 

[edguy99]

Here is a problem from a physics text

An electron (mass 9.11 × 10−31 kg) orbits a hydrogen nucleus at a radius of 5.3 × 10−11 m at a speed of 2.2 × 106 m/s. Find the centripetal force acting on the electron. What type of force supplies the centripetal force?

I'm not interested in the answer, rather I thought that electrons didn't orbit in a Newtonian, viz, predictable fashion. I thought they sort of flew around in their orbits in a manner that only vaguely resembles planetary motion.

The answer tells you that the coulomb force pulling the electron towards the proton matches the force needed to turn the electron and keep it in a stable orbit at that distance. The problem with this model, is how is any other molecule going to bind with this one if it has an electron spinning around it.

The Bohr radius of 5.3 × 10−11 m has another very important property. It represents the distance that of the maximum coulomb force that binds a single electron to a single proton. The energy binding a single electron to a single proton never exceeds 13.6 evolts. It is as if the electron does not feel any force from the proton once it is inside this rather large shell. In chemistry it is common to represent the proton as a shell with the size of a bohr radius.

Try a simple game using these principles of a large proton shell together with a tiny electron called "Shoot the Electron".