Free-body diagram for an electron orbitting a proton.

[seanboy]

1. The distance between the electron and proton in a hydrogen atom is 5.3 x10^-11m. Find the speed of the electron as it orbits the proton.


2. I know how to work this thing out, I'm just having trouble getting started, my free body diagram for the electron (assuming the electron is on the right of the proton) shows a gravitational force going down and an electromagnetic force going left towards the proton. What am I missing?

 

[nasu]

2. I know how to work this thing out

Then never mind the gravity.
It doesn't matter for this problem. It is many (very many) orders of magnitude weaker than the electric force.
You don't need any free body diagram. There is only one force to consider: Coulomb force.

 

[merryjman]

If the electron is moving in a circle, that means it's got a centripetal acceleration of v^2/R. Which force on your FBD is causing this centripetal acceleration? Once you know that, just use F = ma.

 

[DaveC426913]

Trick question?

Electrons haven't orbited protons in almost a century.

 

[merryjman]

Yeah, bro, but you've got to crawl before you can walk. Intro physics always starts with the classical 'orbit' picture before getting into weird quantumish stuff. Clearly this question is not dealing with relativistic or quantum effects.

 

[DaveC426913]

Yeah, bro, but you've got to crawl before you can walk. Intro physics always starts with the classical 'orbit' picture before getting into weird quantumish stuff. Clearly this question is not dealing with relativistic or quantum effects.

Yeah, I can understand that - but why would they use an example that's fundamentally misleading?

It's the equivalent an arithmetic problem that says "Count how many species of fish there are in this picture, including whales."

You can do the math, it's just a silly question...

 

[merryjman]

Hmm, maybe you're right, but every intro physics textbook I've seen (Halliday, Serway, Bueche, Tipler, Giancoli) includes calculations of this nature. I think the reason is that, when Bohr first developed Quantum theory for the H atom, he assumed circular orbits caused by the Coulomb force, but assumed only certain circular orbits were allowed. Even though the model is "wrong," it gave great results for the observed H spectral lines. You could as easily ask why we bother to teach Newton's Universal Law of Gravitation when it's also "wrong" when compared to General Relativity, but can you expect 11th graders to understand GR without some grasp of Newton's Laws?

 

[DaveC426913]

You could as easily ask why we bother to teach Newton's Universal Law of Gravitation when it's also "wrong" when compared to General Relativity,

No it's not. Newton's Laws apply quite nicely in the 99.9% of non-relativistic circumstances we encounter.

but can you expect 11th graders to understand GR without some grasp of Newton's Laws?

I'm not suggesting they teach them GR, I'm suggesting that they find a better example for the math problem.