Free-body diagram for an electron orbitting a proton.

In summary, the conversation discusses the distance between an electron and proton in a hydrogen atom and finding the speed of the electron as it orbits the proton. The importance of considering only the Coulomb force and not gravity is emphasized, and it is explained that the classical 'orbit' picture is used in introductory physics before delving into quantum effects. The use of this example is questioned, but it is explained that it is used because it gave accurate results for observed spectral lines. The comparison to teaching Newton's Laws in relation to General Relativity is also mentioned.
  • #1
seanboy
1
0
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?
 
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  • #2
seanboy said:
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.
 
  • #3
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.
 
  • #4
Trick question?

Electrons haven't orbited protons in almost a century.
 
  • #5
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.
 
  • #6
merryjman said:
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...
 
  • #7
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?
 
  • #8
merryjman said:
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.

merryjman said:
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.
 

1. What is a free-body diagram?

A free-body diagram is a visual representation of the forces acting on an object. It helps to analyze the motion of an object by showing all the external forces acting on it.

2. Why is a free-body diagram useful for studying electron orbiting a proton?

A free-body diagram for an electron orbiting a proton helps to understand the forces that are keeping the electron in its orbit. It also helps to calculate the magnitude and direction of these forces.

3. What forces are shown in a free-body diagram for an electron orbiting a proton?

The two main forces shown in a free-body diagram for an electron orbiting a proton are the electrostatic force and the gravitational force. The electrostatic force is the attraction between the positively charged proton and the negatively charged electron, while the gravitational force is the force of attraction between the two particles due to their masses.

4. Can the distance between the electron and proton affect the forces shown in the free-body diagram?

Yes, the distance between the electron and proton can affect the magnitude of the forces shown in the free-body diagram. As the distance increases, the electrostatic force decreases, while the gravitational force remains constant.

5. How can a free-body diagram for an electron orbiting a proton be used to calculate the velocity of the electron?

By analyzing the forces shown in the free-body diagram and using the equations of motion, the velocity of the electron can be calculated. The electrostatic and gravitational forces act as centripetal forces, keeping the electron in its circular orbit, and the velocity can be determined using the formula v = √(GM/r), where G is the gravitational constant, M is the mass of the proton, and r is the distance between the electron and proton.

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